SCIENCE  OF  LOGIC; 


AN   ANALYSIS 


THE   LAWS' (^-THOUGHT. 


BY   REV.   ASA   MAUAN, 

AUTHOR    OF     AN     "INTELLECTUAL    PHILOSOPHY,'1 
"A   TREATISE    ON    THE    WILL,"     ETC. 


""Words  are  things; 
A  small  drop  of  ink,  falling  like  dew  upon  a  thought, 
Produces  that  which  makes  thousands,  perhaps  millions,  think." 


NEW  YORK: 
A.  S.  BARNES    &   BURR, 

51  &  53  JOHN  STREET. 


*$" 


ttjW 


Entered  according  to  Act  of  Congress,  in  the  year  1856, 
By   ASA    MAHAN, 
In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the  Southern 
District  of  New  York. 


PREFACE. 


Whenever,  in  the  development  of  any  particular  science, 
there  has  been  a  misapprehension  of  its  appropriate  sphere,  and 
especially  when  wrong  principles  have  been  introduced  in  its 
development,  a  reconstruction  of  the  whole  science  is  of  course 
demanded.  The  following  treatise  has  been  prepared  in  view 
of  the  assumption,  that  both  these  defects  exist  in  important 
forms  in  the  common  treatises  on  this  subject — treatises  of 
which  Dr.  Whately's  is  one  of  the  most  prominent  representa- 
tives. Every  one  is  aware,  that  any  given  intellectual  process 
having  for  its  object  the  establishment  of  truth,  may  fail  of  its 
end  for  one  or  more  of  the  three  following  reasons :  1.  The 
process  may  be  based  throughout  upon  a  misconception  of  the 
subject  treated  of.  2.  Invalid  premises  may  be  introduced  as 
the  basis  of  conclusions  deduced.  3.  Or  there  may  be  a  want 
of  connection  between  the  premises  and  the  conclusions  de- 
duced from  them.  All  are  equally  aware,  also,  that  every  valid 
process  is  not  only  free  from  each  of  these  defects,  but  pos- 
sessed of  the  opposite  excellences.  In  examining  any  such 
process,  then,  three  questions  are  or  should  be  always  put,  to 
wit :  Has  the  author  rightly  apprehended  his  subject  ?  Are 
his  premises  sound  ?  Is  there  a  valid  connection  between  his 
premises  and  conclusions  ?  In  answering  such  questions,  every 
one  feels  the  need  of  valid  criteria  by  which  he  can  determine 
whether  the  process  is  or  is  not  valid  in  each  of  these  particu- 
lars, and  in  one  no  less  than  in  either  of  the  others.  The  fol- 
lowing treatise  has  been  prepared  upon  the  assumption,  that 
the  true  and  proper  sphere  of  logic  is  to  furnish  all  these  dif- 
ferent criteria,  and  thus  to  meet  in  full  the  real  logical  necessi- 
ties of  the  human  mind.  The  common  treatises  are  construct- 
ed upon  the  assumption  that  its  true  and  proper  sphere  is  to 
meet  this  want  in  the  last  particular  only,  that  is,  to  furnish 


4  PREFACE. 

criteria  by  which  we  can  distinguish  valid  from  invalid  deduc- 
tions from  given  premises,  and  that  irrespective  of  the  charac- 
ter of  the  premises  themselves.  If  we  are  right  in  our  assump- 
tion— and  the  question  whether  we  are  or  are  not  right,  is  ful- 
ly discussed  in  the  Introduction — then  an  enlargement  of  the 
sphere  of  the  science  beyond  what  is  aimed  at  in  ordinary  trea- 
tises is  demanded,  and  so  far  the  science  needs  a  reconstruction. 
All  such  treatises  that  we  have  ever  heard  of— with  one  ex- 
ception, "  Thomson's  Laws  of  Thought,"  which  has  never  been 
reprinted  in  this  country — have  been  constructed  throughout 
upon  the  assumption,  that  "  all  negative  propositions  and  no 
affirmative,  distribute  the  predicate,"  and  that  in  converting 
a  universal  affirmative  proposition  we  must  change  its  form 
from  a  universal  to  a  particular  ;  as,  "  All  men  are  mortal," — 
"  Some  mortal  beings  are  men."  Let  us  now  suppose  that  as 
far  as  affirmative  propositions  are  concerned,  the  above  princi- 
ples hold  only  in  respect  to  a  single  class,  while,  in  all  other 
cases,  such  propositions  as  well  as  negative  ones  do,  and  from 
the  nature  of  the  relations  between  the  subject  and  predicate 
must,  distribute  the  predicate  as  well  as  the  subject.  In  that 
case  undeniably,  a  reconstruction  of  the  whole  syllogism  is  de- 
manded. Now  the  truth  of  each  of  the  above  statements  can 
be  rendered  demonstrably  evident  on  a  moment's  reflection. 
Why  is  it,  that  in  the  proposition,  for  example,  "  All  men  are 
mortal,"  the  subject  only  is  distributed,  and  that  its  converse 
is,  "  Some  mortal  beings  are  men  ?"  The  reason  is  obvious. 
The  term  men  represents  a  species  of  which  the  term  mortal 
represents  the  genus.  In  other  words,  the  former  term  repre- 
sents what  is  called  an  inferior,  and  the  latter  its  superior,  con- 
ception. The  term  mortal  being  applicable  to  a  larger  number 
of  objects  than  the  term  men,  must  be  understood,  in  the  above 
proposition,  as  representing  only  a  part  of  its  significates.  Such 
proposition,  of  course,  can  be  converted,  but  by  limitation,  that 
is,  changing  its  form  from  a  universal  to  a  particular.  It  is  only 
in  reference  to  this  one  class  of  propositions,  however,  that  the 
principles  under  consideration  do  or  can  hold.  When  the 
sphere  of  the  subject  and  predicate  are,  from  the  nature  of  the 
terms  themselves,  equal — as  they  are,  in  all  cases  but  in  reference 
to  the  single  class  referred  to — then  affirmative  propositions  dis- 
tribute the  predicate  on  the  same  principles  that  negative  ones 
do.     We  will  mention  here  for  illustration  but  a  single  class  of 


PREFACE.  5 


propositions  of  this  kind — the  mathematical.  In  every  univer- 
sal affirmative  proposition  throughout  the  entire  range  of  this 
science,  the  predicate  as  well  as  the  subject  is  distributed ;  the 
converse  as  well  as  the  exposita  being  universal  also.  This 
holds  equally  in  regard  to  the  principles  and  subsequent  deduc- 
tions of  this  science.  What  is  the  converse,  for  example,  of 
such  propositions  as  the  following  ?  "  Things  equal  to  the 
same  tilings  are  equal  to  one  another," — "  The  square  of  the 
hypothenuse  of  a  right-angled  triangle  is  equal  to  the  sum  of 
the  squares  of  the  two  sides," — "6+4  —  10," — "X  =  Z,"  &c.  ? 
The  whole  science  of  logic  has  been  constructed  upon  principles 
of  distribution  and  conversion,  which  would  utterly  mislead 
us,  if  applied  to  any  of  the  universal  affirmative  propositions 
throughout  the  entire  range  of  the  science  of  the  mathematics, 
or  to  any  propositions  but  one  of  the  single  class  above  named. 
In  respect  to  the  different  figures  of  the  syllogism,  also,  it  has 
been  laid  down  as  holding  universally,  that  the  second  yields 
only  negative,  and  the  third  only  particular,  conclusions.  This 
also  holds  true  when,  and  only  when,  the  propositions  belong 
to  the  single  class  above  named.  In  all  other  cases,  we  can  ob- 
tain universal  affirmative  or  negative  conclusions,  in  each  and 
all  the  figures  alike.    Take  the  following  as  examples : 

FIG.  I.  FIG.  II.  FIG.  III. 

M=X ;  X=M ;  M=X ; 

Z  =  M;  Z=M;  M=Z ; 

.-.  Z  =  X.  .-.  Z=X.  .-.  Z=X. 

Every  one  will  perceive  at  once  that  each  of  the  above  syllo- 
gisms is  of  equal  validity,  and  that  the  converse  of  the  conclu- 
sion is  in  each  case  universal,  as  well  as  the  exposita. 

The  dictum,  too,  under  which  the  syllogism  has  been  con- 
structed will  be  found  to  be  applicable  only  to  arguments  con- 
structed entirely  from  the  single  class  of  propositions  named. 
These  facts  being  undeniable,  every  one  will  perceive  that  sci- 
ence demands  a  reconstruction  of  the  syllogism  throughout. 
This  we  have  attempted  to  do,  and  trust  we  have  accomplished 
to  the  satisfaction  of  all  who  shall  acquaint  themselves  with  the 
following  treatise.  Before  venturing  to  give  our  deductions  in 
the  important  particulars  now  before  us  to  the  public,  we  sub- 
mitted them  to  numbers  of  scientific  men  in  whose  judgment 
we  have  great  confidence.  From  these  we  have  received  such 
expressions  of  approbation  as  to  inspire  us  with  the  assurance, 


V 


6  PREFACE. 

that  these  deductions  will  stand  the  test  of  the  most  rigid  scien- 
tific scrutiny,  which  is  most  cordially  invited. 

The  doctrine  of  fallacies,  treated  of  in  Part  II.,  we  have 
aimed  to  simplify  by  proper  definitions,  logical  division,  and 
arrangement  of  the  whole  subject,  so  as  to  render  the  doctrine 
luminous  throughout  and  its  principles  of  ready  application  in 
the  reader's  mind. 

Almost  no  portion  of  the  treatise  does  the  author  regard  as 
of  higher  importance  than  the  doctrine  of  method,  as  eluci- 
dated in  Part  III.  We  judge  that  the  public  will  perceive 
that  an  important  scientific  want  is  there  met. 

In  furnishing  the  examples  presented  in  Part  TV.  we  have 
had  two  special  objects  in  view — to  present  fundamental  sug- 
gestions in  regard  to  important  questions  in  science ;  and  to 
furnish  examples  for  criticism  of  corresponding  importance. 
If,  in  any  case  or  in  all  cases,  it  should  turn  out  that  we  have 
erred  in  reasoning  or  in  any  other  particular,  and  the  error 
shall  be  discovered  by  the  application  of  the  principles  previous- 
ly elucidated,  the  great  end  of  the  work  is  answered,  and  the 
examples  will  still  have  their  proper  place  in  the  work,  just  as 
they  would  if  cited  from  another  author  as  examples  of  fallacy 
in  reasoning,  or  of  error  or  defect  in  any  other  particular. 

In  the  perusal  of  the  following  treatise  the  public  will  per- 
ceive that  we  are  much  indebted  to  three  authors — Mr.  Thom- 
son, whose  work  we  had  never  seen  till  we  had  progressed  in 
our  own  to  the  very  place  where  important  citations  from  his 
first  appear — Kant,  whose  treatise,  in  our  judgment,  excels  by 
far  in  important  respects  any  other  that  we  have  met  with — 
and  Sir  William  Hamilton,  to  whom  the  science  of  logic,  and 
the  author  of  this  treatise  especially,  is  more  indebted  than  to 
any  other  author — the  father  of  the  science,  of  course,  excepted. 
It  is  with  the  utmost  gratification  that  we  would  record  the 
fact,  that  in  almost  every  particular  in  which  we  have  departed 
from  the  beaten  track  in  the  development  of  the  science,  we 
are  sustained  throughout  by  such  high  authority  as  Sir  Wil- 
liam Hamilton.  With  these  suggestions,  the  following  treatise 
is  commended  to  the  careful  examination  and  candid  criticism 
of  the  public. 


CONTENTS. 


PAGE 

Introduction 17 

Necessity  of  a  correct  definition  of  Logic 17 

All  things  occur  according  to  rules 18 

'  Logic  defined 19 

Eelations  of  Logic  to  other  sciences 19 

The  idea  of  Logic  developed  in  a  form  still  more  clear  and  distinct 20 

Divisions  of  Logic 21 

Correctness  of  the  ahove  definition  verified 21 

Logic  as  distinguished  from  Esthetics 24 

Accordance  of  the  above  conception  of  Logic  with  that  given  by  Kant.  25 
Accordance  of  the  above  idea  of  Logic  with  that  set  forth  by  Sir  Wil- 
liam Hamilton 26 

Inadequate  and  false  conceptions  of  this  science 27 

1.  The  syllogistic  idea 27 

2.  Conceptions  of  Dr.  Whately  and  others 32 

3.  The  idea  that  "  the  adequate  object  of  Logic  is  language" 33 

General  division  of  topics 35 


PART  I.— THE  ANALYTIC. 

CHAPTER  I. — Analytic  of  Conceptions  and  Terms.  - 

Section  I. — Of  Conceptions 37 

Conceptions  defined 37 

Origin  and  constituent  elements  of  Conceptions 37 

Error  commences,  not  with  Intuitions,  but  Conceptions 39 

Universal  characteristics  of  all  valid  and  invalid  Conceptions 39 

Spontaneous  and  Reflective  Conceptions 40 

First  and  second  Conceptions 40 

Matter  and  sphere  of  Conceptions 41 

Individual,  generic  or  generical,  and  specific  or  specifical  Conceptions .  42 

Highest  genus  and  lowest  species 42 

Empirical  and  rational  Conceptions 43 

Presentative  and  representative  Conceptions 45 


8  CONTENTS. 

Abstract  and  concrete  Conceptions 45 

Positive,  privative,  and  negative  Conceptions 46 

Conceptions  classed  under  the  principle  of  unity,  plurality,  and  totality  46 

Inferior  and  superior  Conceptions 46 

Concrete  and  characteristic  Conceptions 47 

Laws  of  thought  pertaining  to  the  validity  of  Conceptions 47 

Particular,  general,  and  abstract  Conceptions 48 

Individual,  specifical,  and  generical  Conceptions 48 

Presentative  and  representative  Conceptions. 49 

Concrete  and  characteristic  Conceptions 49 

Inferior  and  superior  Conceptions 50 

Empirical  and  rational  Conceptions 50 

Section  II.— Of  Terms 51 

Singular  and  common  Terms. — Significates 51 

Eelations  of  Logic  to  Terms 51 

CHAPTEK  II.— Of  Judgments. 

Section  I. — Of  Judgments  considered  as  Mental  States 52 

Matter  and  form  of  Judgments 52 

Quantity  of  Judgments,  universal,  particular,  individual  or  singular  .  53 

Quality  of  Judgments,  affirmative,  negative,  indefinite 54 

Relation  of  Judgments,  categorical,  hypothetical,  and  disjunctive 54 

Remarks  on  these  Judgments 55 

Categorical  Judgments 55 

Hypothetical  Judgments 56 

Disjunctive  Judgments 58 

Modality  of  Judgments,  problematical,  assertative,  contingent,  neces- 
sary (appodictical) — Remarks 58,  59 

Theoretical  and  practical  Judgments 60 

Demonstrable,  and  indemonstrable  or  intuitive  Judgments 61 

Analytical  and  synthetical  Judgments 61 

Criteria  of  all  first  Truths 63 

Kant's  definition  of  analytical  and  synthetical  Judgments 63 

Tautological,  identical,  and  implied  Judgments 64  .. 

Axioms,  Postulates,  Problems,  and  Theorems 65 

Corollarys,  Lemmas,  and  Scholia ( 66 

Criteria  of  Judgments,  or  characteristics  of  all  valid  Judgments 66 

General  Criteria 67 

Particular  and  special  Criteria 67 

Judgments  relative  to  all  valid  Conceptions 67 

Individual  (single),  Particular,  and  Universal  Judgments 68 

Individual  Judgments  (affirmative) 68 

Individual  Judgments  (negative) 69 


CONTENTS.  9 


Universal  Judgments  (affirmative) 71 

Universal  Judgments  (negative) 71 

Judgments  pertaining  to  the  objects  of  inferior  and  superior  Concep- 
tions   72 

Judgments  pertaining  to  the  objects  of  characteristic  Conceptions  (af- 
firmative)    73 

Judgments  relative  to  objects  of  characteristic  Conceptions  (negative) . .  73 

Hypothetical  Judgments 74 

Hypothetical  Judgments  classed 74 

Criteria  of  such  Judgments 74 

Disjunctive  Judgments 76 

Section  II. — Of  Propositions 77 

Quality  and  Quantity  of  Propositions,  &c 77 

Distribution  of  Terms 78 

Of  Opposition 80 

Of  the  Conversion  of  Propositions 82 

Quantification  of  the  Predicate 84 

Parti-partial  Negation , 87 

Criteria  by  which  Propositions  properly  falling  under  these  different 

classes  may  be  distinguished  from  each  other 90 

CHAPTER  III. — Analytic  of  Arguments  or  Syllogisms. 

Section  I. — Argument  defined  and  elucidated 94 

Diverse  Forms  of  the  Syllogism 96 

Section  II. — The  Analytic  and  Synthetic  Syllogism 96 

These  distinct  forms  of  the  Syllogism  elucidated 96 

Section  III. — Figured  and  Unfigured  Syllogisms 99 

Principles  and  Laws  of  the  Unfigured  Syllogism ., . . .  100 

The  Canon  of  this  Syllogism 100 

General  Remarks  upon  this  form  of  the  Syllogism 102 

Section  IV.— The  Figured  Syllogism 103 

This  form  defined 103 

Common  assumption  on  the  subject 103 

Influence  of  Assumptions 104 

Principles  determining  the  distribution  of  the  Predicate .  104 

Fundamental  mistake  in  developing  the  science  of  Logic '. 106 

Division  of  the  present  subject 107 

I.  Those  forms  of  the  Syllogism  which  have  been  commonly  treated  of 
as  including  all  forms  of  the  categorical  argument,  to  wit :  those 
forms  in  which  the  terms  employed  are  related  to  each  other  as 

Inferior  and  Superior  Conceptions 108 

Preliminary  Remarks  upon  this  Form  of  the  Figured  Syllogism 108 

1* 


10  CONTENTS. 

Only  proximate  conclusions  obtained 108 

1.  The  principle  of  Extension  and  Intension,  or  of  Breadth  and 

Depth,  as  applied  to  the  Syllogism 109 

2.  Import  of  Judgments  (Extension  and  Intension — Naming) 110 

3.  Direct  and  indirect  conclusion. .    112 

4.  Character  of  all  the  propositions  employed  in  this  form  of  the 

Syllogism 113 

Letters  to  be  employed 113 

Canon  and  Laws  of  this  Form  of  the  Syllogism — Conditions  on  which 
we  can  obtain  the  different  classes  of  Conclusions  above  named  ; 

that  is,  A,  I,  E,  0 113 

Universal  Affirmative  Conclusions 113 

Universal  Negative  Conclusions 114 

Particular  Affirmative  Conclusions 114 

Particular  Negative  Conclusions 115 

All  valid  Conclusions  deduced  upon  principles  which  accord  with  those 

above  elucidated 116 

Analysis  of  the  above  relations 117 

The  Canon  of  this  Syllogism 119 

Moods  of  the  Syllogism 120 

Figure  of  the  Syllogism— Form  defined 121 

Number  of  figures  of  the  Syllogism 121 

Major  and  Minor  Terms  and  Premises 122 

Order  of  the  Premises 122 

Final  abolishment  of  the  Fourth  Figure 123 

Opinions  of  Logicians  upon  the  subject 123 

Our  Eeasons  for  the  abolition  of  this  Figure 124 

Special  Characteristics  and  Canon  of  each  of  the  three  Figures 126 

Figure  1 126 

The  Canon  illustrated. 127 

Figure  II 128 

Canon  of  this  Figure 130 

Figure  ni 131 

Canon  of  this  Figure 132 

Absurdity  of  reducing  the  Syllogisms  of  the  other  Figures  to  the  first.  132 

Nature  of  the  Conclusions  obtained  in  this  form  of  the  Syllogism 133 

Kind  of  arguments  which  appropriately  belong  to  the  different  Figures  135 

A  more  brief  view  of  this  subject I 138 

A  scientific  determination  of  the  real  number  of  Legitimate  Moods  in 

this  form  of  the  Syllogism 138 

Conditions  of  valid  deductions  of  any  kind  in  this  form  of  the  Syl- 
logism    139 

Universal  affirmative  conclusions 139 

Particular  affirmative  conclusions 139 


CONTENTS.  11 


Universal  negative  conclusions 140 

Particular  negative  conclusions 141 

The  number  of  Moods 142 

Similar  determination  of  the  number  of  Moods  in  each  Figure 142 

1.  Syllogisms  allowable  in  the  First  Figure 142 

2.  Moods  or  Syllogisms  allowable  in  the  Second  Figure 143 

3.  Allowable  Moods  in  the  Third  Figure. 144 

II.  That  department  of  the  Figured  Syllogism  in  which  there  is,  not 

only  in  Negative  but  in  Affirmative  Propositions,  the  distribution 

of  the  Predicate  as  well  as  of  the  Subject 145 

Propositions  of  this  kind  classified 146 

Additional  Syllogisms  illustrative  of  the  above  classes  of  Judgments. . .   148 

1.  Syllogisms  constituted  of  Substitutive  Judgments 149 

2.  Quantitive  Judgments 149 

3.  Correlative  Judgments 149 

4.  Judgments  falling  under  the  principle  of  likeness  and  unlikeness  149 
6.  Proportional  Judgments 150 

Table  of  Logical  Judgments 150 

Affirmatives 150 

Negatives 151 

Of  opposition  and  conversion  of  Judgments 151 

Canon  of  this  form  of  the  Syllogism 152 

Special  Characteristics  of  this  Form  of  the  Syllogism 152 

III.  The  two  Forms  of  the  Syllogism  combined 154 

Table  of  all  the  Legitimate  Moods  in  all  figures 155 

A  mode  of  Notation 156 

Equivalent  Syllogisms 159 

Sir  William    Hamilton's   Scheme   of   Moods   and    Figures  of   Syllo- 
gisms  161,  162 

Table  of  Moods 164 

Sum  of  all  the  valid  Moods  in  each  Figure 165 

Euler's  System  of  Notation 165 

Sir  William  Hamilton's  Special  Canons  of  the  different  Figures 166 

1.  Canon  of  the  First  Figure 166 

2.  Canon  of  the  Second  Figure 166 

3.  Canon  of  the  Third  Figure 167 

Canons  and  Diverse  Forms  of  the  Figured  Syllogism  elucidated 167 

Proper  sphere  and  application  of  Aristotle's  dictum 169 

Section  V. — The  Conditional  Syllogism 170 

The  appropriate  sphere  of  the  Conditional  Syllogism 172 

Section  VI. — The  Disjunctive  Syllogism 175 

Circumstances  in  which  the  Disjunctive  Syllogism  should  be  used 175 

Section  VII.— The  Dilemma 177 

Circumstances  which  require  the  use  of  this  form  of  the  Syllogism 177 


12  CONTENTS. 

Section  VIII. — The  Deductive  and  Inductive  Syllogisms 179 

Section  IX. — Syllogisms  of  Induction  and  Analogy 183 

Demonstrative,  inductive,  and  analogical  reasoning  distinguished. . . .  183 

Canon  of  the  Inductive  Syllogism 187 

General  Characteristics  of  all  facts  or  principles  which  are  to  be  as- 
sumed as  Causes  or  Laws 187 

Verification  of  Inductions 193 

Canon  of  the  Syllogism  of  Analogy 195 

When  the  Syllogism  of  Analogy  has  the  greatest  force 196 

The  Enthymeme 196 

Section  X. — The  Sorites,  or  Chain  Syllogism — Term  defined 197 

Principles  on  which  this  Form  of  Seasoning  depends 197 

The  Sorites  can  have  but  one  particular,  and  one  negative,  premise. . .  199 

Forms  of  this  kind  of  argument 199 

Section  XL — Syllogism  of  Chance — this  Syllogism  defined 201 

Principle  which  governs  such  calculations 201 

Section  XII. — Immediate  and  Mediate  Syllogisms 202 

Section  XIII. — The  Prosyllogism  and  Episyllogism 203 

Section  XIV. — Syllogism  of  Classification 204 

Principles  and  Laws  of  this  Form  of  the  Syllogism 204 

Concluding  Explanations 206 


PART  n.— THE  DIALECTIC,  OR  DOCTRINE  OF  FAL- 
LACIES. 

Fallacy  defined 209 

Fallacies  where  found 209 

The  ultimate  cause  and  source  of  Error 210 

CHAPTER  I. — Invalid  Conceptions. 

Sources  of  Invalid  Conceptions , 211 

CHAPTER  II.— The  Dialectic— Invalid  Judgments. 

Section  L— Problematical  Judgments  assumed  as  First  Truths 216 

Assumption  that  a  thing  cannot  act  where  it  is  not 217 

The  assumption  that  our  knowledge  of  matter  is  exclusively  mediate. .  217 

Fundamental  and  opposite  Assumptions  of  Materialism  and  Idealism . .  218 

Assumption  pertaining  to  the  Origin  of  our  idea  of  Cause  and  Effect . . .  220 

"The  Eternal  Now"  of  Theology 223 

Assumption  pertaining  to  the  Divine  Personality,  &c 224 

Section  II. — Invalid  Assumptions  pertaining  to  Matters  of  Fact 226 


CONTENTS.  13 

CHAPTER  III. — The  Dialectic— Fallacies  of  Reasoning. 

Fallacies  in  Reasoning '.   232 

General  Characteristics  of  all  Invalid  Deductions 233 

Section  I. — Conclusions  deduced  from  Premises  which  prove  nothing.  233 

Arguing  from  two  Negative  or  two  Particular  Premises 233 

Drawing  positive  conclusions  from  Problematical  Premises 234 

Petitio  Principii 234 

Arguing  in  a  Circle 235 

Deducing  positive  conclusions  from  Premises  known  to  be  invalid  in 

themselves 236 

Leap  in  Logic 238 

Proving  too  much 240 

Inferring  the  falsity  of  the  conclusion  from  that  of  the  premise,  or  the 

truth  of  the  premise  from  the  truth  of  the  conclusion 240 

Fallacy  of  References 241 

Fallacies  connected  with  the  use  of  the  Middle  Term 242 

Conditional  Syllogisms  whose  Conditional  Premises  are  void  of  Logical 

Consequence 247 

Disjunctive  Syllogisms  whose  Disjunctive  Premises  are  void  of  Logical 

Consequence 248 

Fallacies  arising  from  the  use  of  Invalid  Dilemmas 251 

Conclusions  based  upon  false  Analogies , 252 

Section  II. — Conclusions  deduced  from  Premises  which  come  short  of 

proving  said  Conclusions 253 

Drawing  a  universal  conclusion,  where  only  a  particular  is  allowable.  253 
Proving  a  part  of  aconclusion  and  then  assuming  the  whole  as  established  254 

Fallacy  of  Objections 255 

Assumption  of  Probabilities 255 

Section  III. — Conclusions  deduced  from  Premises  which  prove  not  those 

really  sought  to  be  proved,  but  certain  other  and  irrelevant  ones . .  257 

Ignoratio  elenchi,  or  Irrelevant  Conclusion 257 

Suppressing  the  Conclusion 263 

Argumentum  ad  hominem 264 


PART  EX— THE  DOCTRINE  OF  METHOD. 

Terms  defined 267 

Means  by  which  the  Logical  Perfection  of  Thought  may  be  secured  . . .  267 

Conditions  on  which  these  ends  may  be  secured 268 

Section  I.—  Logical  Perfection  of  Thought  as  promoted  by  proper  Defi- 
nition and  Exposition 268 

Design  of  Definition  and  Exposition 268 


14  CONTENTS. 

Proper  objects  of  Definition  and  Exposition 268 

Characteristics  of  all  Correct  Definitions 269 

Characteristics  of  Defective  Definitions 271 

Elements  which  enter  into,  and  are  excluded  ffom,  all  Perfect  Definitions  272 

Characteristic,  Generical,  Specifical,  and  Individual  Conceptions 272 

Definitions  of  Propositions 273 

True  use  of  Affirmation  and  Negation  in  Definition 273 

Nominal  and  Real  Definitions 274 

Subjective  and  Objective  Definitions 274 

Examples  of  Perfect  and  Imperfect  Definitions 273 

The  term  Judgment  defined 275 

Moral  Action  defined 276 

Moral  Law  defined 277 

A  Moral  Agent  defined : 278 

Ultimate  Intuition  defined 278 

The  term  God  defined 279 

Section  II. — Promotion  of  the  Logical  Perfection  of  Thought  by  means 

of  the  Logical  Division  of  Conceptions  or  Subjects — Terms  defined  280 

Universal  Rules  for  Logical  Division 281 

Codivision  and  Subdivision 282 

The  Fragmentary  as  opposed  to  the  Real  Logical  Division  of  Subjects. .   283 
Section  III. — The  Promotion  of  the  Logical  Perfection  of  Thought  by 

means  of  a  proper  arrangement  of  the  parts  of  the  Subject  treated  of  283 

Terms  defined — Analytic  and  Synthetic  Order  of  Thought 283 

Canons  of  Order 284 

Section  IV. — Miscellaneous  Topics  bearing  upon  our  present  Inquiries 

—The  Doctrine  of  Method 285 

Characteristics  of  every  well-conducted  Argument 285 

Methods  of  Proof — the  Direct  and  Indirect,  and  the  two  united  in  the 

same  Argument 286 

Characteristics  of  all  Forms  of  Valid  Evidence 287 

Forms  of  Evidence  classified 287 

Characteristics  of  all  Forms  of  Valid  Proof 288 

The  Mathematical  Form 288 

Reasoning  from  Facts  to  General  Conclusions,  or  from  one  Fact  to 

another 289 

The  True  and  Proper  Method  of  determining  the  Character  and  Validi- 
ty of  any  given  Argument 298 

Example  in  illustration 291 

Method  or  Forms  of  Proving  a  given  Proposition  false 293 

Method  or  Forms  of  Refuting  any  given  Argument — Terms  defined . . .  294 

Objections  to  a  given  Hypothesis  when  valid 295 

Method  of  Refuting  Objections,  or  the  Forms  in  which  they  may  be  re- 
futed    296 


CONTENTS. 


PART  IV.— APPLIED  LOGIC. 

*"  The  Anglo-Saxon  and  German  Methods  of  developing  Thought 298 

Reasons  for  this  difference 299 

-  Illustration  1.— Systems  of  Natural  Theology  developed  according  to 

these  two  Methods 299 

"     Illustration  2. — Systems  of  Intellectual  Philosophy  developed  according 

to  the  Principles  of  these  two  Methods 300 

The  Character  of  any  System  of  Intellectual  Philosophy  which  shall 

meet  the  fundamental  wants  of  the  present  age ". . .  304 

-  Error  of  Mr.  Mill  in  regard  to  the  Syllogism 305 

Error  of  Mr.  Mill  in  regard  to  the  Nature  of  all  Forms  of  Inference 307 

Mr.  Mill's  position  that  "the  syllogism  is  not  the  type  of  reasoning, 

but  a  test  of  it" 309 

Exclusive  Condition  on  which  we  can  legitimately  reason  from  particu- 
lars to  particulars 310 

Relations  of  the  Syllogism  to  the  Discovery  of  Truth 311 

The  Great  Problem  in  Philosophy  according  to  Kant 312 

Kant's  Solution  of  this  Problem 313 

Errors  of  Kant  in  the  solution  of  this  Problem 314 

The  Sensational  Theory  of  External  Perception 320 

The  Great  Problem  in  Philosophy  of  the  Present  Age 322 

Proposed  solution  of  this  Problem 323 

Distinction  between  Presentative  and  Representative  Knowledge 323 

The  Formulas  stated 324 

These  Formulas  and  Test  verified 326 

Bearing  of  these  Formulas  upon  Systems  of  Ontology 327 

—-"Character  and  claims  of  Empiricism,  Materialism,  Idealism,  and  Real- 
ism, as  systems  of  philosophy 327 

General  Remarks  upon  these  Systems 331 

^  Dogmatism,  Skepticism,  Positiveism,  and  Free-Thinking 333 

Conditions  of  the  Possibility  of  Science  in  any  Particular  Department 

of  Thought 334 

Bearings  of  the  Sensational  Theory  of  Perception 335 

Conditions  on  which  the  Proposition,  "God  exists,"  can  legitimately 

take  its  place  as  an  undeniable  Truth  of  Science 337 

The  Theistic  Formulas \  .  338 

The  Disjunctive  Argument  for  the  Theistic  Hypothesis 339 

The  ultimate  principles  on  which  the  hypotheses  of  Theism,  Skepti- 
cism, and  Anti-Theism  in  all  its  forms,  rest 340 

Common  Theistic  Syllogism  and  Argument 341 

Influence  of  the  Hypothesis,  that  there  are  different  kinds  of  proof  of 
the  being  of  God 349 


16  CONTENTS. 

The  two  Aberdeen  prize  essays  denominated  "Christian  Theism," 

and  "  Theism" 351 

Professor  Tulloch's  Treatise  (Theism) v. .  352 

Professor  Tulloch's  professed  Demonstration  of  his  Major  Premise 353 

Our  Author's  Direct  and  Positive  Argument 357 

Mr.  Thomson's  Treatise  (Christian  Theism) 364 

The  Dogma  that  our  Idea  of  God  is  purely  Negative 376 

The  real  Basis  of  all  Valid  Scientific  Procedures 377 

The  Dogma  that  our  Knowledge  of  Nature  is  confined  to  Phenomena, 

and  does  not  pertain  to  Substances  themselves 378 

The  Dogma  that  Individual  Conceptions  pertain  to  Objects,  and  gen- 
eral ones  only  to  the  Mind  which  forms  them 379 

The  idea  of  a  "  Positive  Philosophy' ' 380 

False  Methods  in  Philosophy 386 


INTRODUCTION. 


Necessity  of  a  correct  definition  of  Logic 

Every  science  has  a  sphere  peculiar  to  itself.  Its  end  or 
aim  also,  in  the  occupancy  of  that  sphere,  is  equally  special 
and  peculiar.  The  mathematics,  for  example,  have  an  exclu- 
sive sphere,  end,  and  aim,  and  metaphysics  others  equally 
special  and  exclusive.  To  enter  intelligently  and  with  the  ra- 
tional hope  of  the  highest  profit,  upon  the  study  of  any  par- 
ticular science,  its  peculiar  sphere,  and  special  aim  in  the  occu- 
pancy of  the  same,  must  be  distinctly  apprehended.  Now; 
while  the  sphere  and  aim  of  most  of  the  sciences  have  been 
definitely  determined,  the  opposite  is  most  strikingly  true  in 
regard  to  logic.  It  would  be  difficult  to  name  any  two  phi- 
losophers, with  the  exception  perhaps  of  Kant  and  Sir  Wil- 
liam Hamilton,  who  fully  agree  in  their  ideas  and  definitions 
of  this  science.  By  some  it  is  defined  as  the  art,  by  others 
as  the  science,  and  by  others  still,  as  "  the  science  and  art  of 
reasoning.'1''  According  to  Sir  William  Hamilton,  "the  laws 
of  thought,  and  not  the  laws  of  reasoning,  constitute  the  ade- 
quate object  of  the  science."  This  definition,  as  the  reader 
will  readily  perceive,  is  really  identical  with  the  following  given 
by  Kant :   "  This  science  of  the  necessary  laws  of  the  under- 


18  INTRODUCTION. 

standing  and  of  reason  in  general,  or  of  (what  amounts  to  the 
same  thing)  the  mere  form  (laws)  of  thinking  in  general,  we 
name  logic."  These  last  two  definitions,  as  we  apprehend 
them,  we  regard  as  strictly  correct,  and  as  presenting  the 
only  true  and  adequate  conception  of  the  proper  sphere  and 
aim  of  the  science.  "We  will  now  proceed  to  elucidate  the 
ahove  definitions  as  we  understand  tnem,  and  to  do  so  by  giv- 
ing our  own  independent  definition  of  the  science.  As  pre- 
paratory to  this  end,  we  would  invite  special  attention  to 
the  following  extract  from  our  own  work  on  Intellectual  Phi- 


"  All  things  occur  according  to  rules, 

" '  Every  thing  in  nature,'  says  Kant,  and  this  is  one  of  his 
most  important  thoughts,  'as  well  in  the  inanimate  as  in  the 
animate  world,  happens,  or  is  done,  according  to  rules,  though 
we  do  not  know  them.  Water  falls  according  to  the  laws  of 
gravitation,  and  the  motion  of  walking  is  performed  by  ani- 
mals according  to  rules.  The  fish  in  the  water,  the  bird  in 
the  air,  move  according  to  rules.' 

"  Again :  '  There  is  nowhere  any  want  of  rule.  When  we 
think  we  find  that  want,  we  can  only  say  that,  in  this  case,  the 
rules  are  unknown  to  us.' 

"  The  exercise  of  our  intelligence  is  not  an  exception  to  the 
above  remark.  When  we  speak,  our  language  is  thrown  into 
harmony  with  rules,  to  which  we  conform  without,  in  most  in- 
stances, a  reflective  consciousness  of  their  existence.  Grammar 
1b  nothing  but  a  systematic  development  of  these  rules.  So 
also,  when  we  judge  a  proposition  to  be  true  or  false,  or  to  be 
proved  or  disproved,  by  a  particular  process  of  argumentation, 
or  when  we  attempt  to  present  to  ourselves,  for  self-satisfac 


INTEODUCTION.  19 


tion,  or  to  others  for  the  purpose  of  convincing  them,  the 
grounds  of  our  own  convictions — that  is,  when  we*  reason,  our 
intelligence  proceeds  according  to  fixed  rules.  When  we  have 
judged  or  reasoned  correctly,  we  find  ourselves  able,  on  reflec- 
tion, to  develop  the  rules  in  conformity  to  which  we  judged  and 
reasoned,  without  a  distinct  consciousness  of  the  fact.  In  the 
light  of  these  rules  we  are  then  able  to  detect  the  reason  and 
grounds  of  fallacious  judgments  and  reasonings. 

"Logic  defined. 

"  The  above  remarks  have  prepared  the  way  for  a  distinct 
statement  of  the  true  conception  of  logic.  It  is  a  systematic 
development  of  those  rules  in  conformity  to  which  the  univer- 
sal intelligence  acts,  hi  judging  and  reasoning.  Logic,  accord- 
ing to  this  conception,  would  naturally  divide  itself  into  two 
parts — a  development  of  those  rules  to  which  the  intelligence 
conforms  in  all  acts  of  correct  judgment  and  reasoning,  and 
a  development  of  those  principles  by  which  false  judgments 
may  be  distinguished  from  the  true.  A  treatise  on  logic,  in 
which  the  lawTs  of  judging  and  reasoning  are  evolved  in  strict 
conformity  to  the  above  conception,  would  realize  the  idea  of 
science,  as  far  as  this  subject  is  concerned.  Logic,  to  judging 
and  reasoning,  is  what  grammar  is  to  speaking  and  writing. 
Logic  pertains  not  at  all  to  the  particular  objects  about  which 
the  intelligence  is,  from  time  to  time,  employed,  but  to  the 
rules  or  laws  in  conformity  to  which  it  does  act,  whatever  the 
objects  may  be. 

"  Relations  of  Logic  to  other  sciences. 

"  In  the  chronological  order  of  intellectual  procedure,  logic  is 
preceded  by  judging  and  reasoning,  just  as  speaking  and  writ- 


20  INTEODUCTIOST. 

ing  precede  grammar.  '  In  the  logical  order,  however,  it  is 
the  antecedent  of  all  other  sciences.  In  all  sciences  the  in- 
telligence, from  given  data,  judges  in  regard  to  truths  resulting 
from  such  data :  we  also  reason  from  such  data  for  the  estab- 
lishment of  such  truths.  Logic  develops  the  laws  of  thought 
which  govern  the  action  of  the  intelligence  in  all  such  pro- 
cedures. As  a  science,  it  is  distinct  from  all  other  sciences. 
Yet,  it  permeates  them  all,  giving  laws  to  the  intelligence  in 
all  its  judgments  and  reasonings,  whatever  the  objects  may  be 
about  which  it  is  employed." 

The  idea  of  Logic  developed  in  a  form  still  more  clear  and 
distinct. 

It  will  readily  be  perceived,  we  judge,  that  the  above  defini- 
tions and  statements  have  made  a  somewhat  near  approach,  to 
say  the  least,  to  the  true  idea  of  the  science  under  consideration. 
To  place  the  subject  in  a  light  still  more  clear  and  distinct, 
we -would  observe,  that  there  are  certain  cognitions,  certain  pro- 
cesses of  thought,  which  are  universally  regarded  as  valid  for 
the  truth  of  what  is  therein  referred  to.  We  examine,  for  ex- 
ample, the  process  of  thought  (statements  and  demonstrations) 
by  which  we  are  conducted  to  the  conclusion,  that  the  square 
of  the  hypothenuse  of  a  right-angled  triangle,  is  equal  to  the 
sum  of  the  squares  of  its  two  sides.  We  affirm  that,  on  ac- 
count of  what  is  contained  in  said  process,  that  proposition  is 
to  be  held  as  true ;  in  other  words,  the  process  itself  is  valid 
for  the  truth  of  what  is  therein  referred  to.  On  the  other 
hand,  there  are  other  processes  which  are  not  thus  valid. 
What  is  true  is  sometimes  professedly  established  by  pro- 
cesses not  at  all  valid  for  its  reality,  and  through  other  pro- 
cesses what  is  not  true  is  often  affirmed  to  have  been  estab- 


INTRODUCTION.  21 


lished  as  a  reality.  All  processes  of  the  first  class  are  held  as 
valid,  and  the  two  last  named  are  regarded  as  invalid  pro- 
cedures of  the  intelligence.  In  each  process  alike,  the  valid, 
as  well  as  the  invalid,  the  intelligence  has  acted  in  accordance 
with  certain  fixed  laws  or  principles,  which  we  are  able  to  de- 
termine. To  develop,  that  is,  determine,  define,  and  elucidate 
these  laws,  and  thus  present  universal  criteria  of  valid  and  in- 
valid procedures  of  the  intelligence,  when  the  object  of  such 
procedure  is  truth,  is,  as  we  understand  the  subject,  the  true 
and  exclusive  sphere  and  aim  of  logic  as  a  science. 

»  Divisions  of  Logic 

Logic,  as  a  science,  consequently  divides  itself  into  two  parts : 
1.  A  systematic  development  of  those  principles  or  laws  to 
which  the  intelligence  accords  in  all  valid  intellectual  processes, 
processes  whose  object  is  truth.  2.  A  similar  development  of 
those  principles  to  which  the  intelligence  conforms,  in  all  in- 
valid processes  of  the  class  under  consideration.  Such  is  logic 
as  a  science,  in  the  sense  in  which  we  understand  the  subject 
and  in  which  we  shall  attempt  to  realize  the  idea.  Xo  one 
will  dissent  from  the  above  conception,  but  upon  a  single  as-, 
sumption,  to  wit,  that  the  sphere  assigned  to  the  science  is  too 
extensive,  that  sphere  including  all  that  has  been  commonly  re- 
ferred to  the  science  and  some  things  else  supposed  not  to  per- 
tain to  it.  That  this  is  the  true  and  proper  sphere  of  the 
science,  we  argue  from  the  following  considerations. 

Correctness  of  the  above  definition  verified. 

1.  The  above  definition  gives  a  perfect  unity  and  definiteness 
to  our  conceptions  of  the  science,  the  very  unity  and  definite- 


22  INTRODUCTION. 

ness   which   characterize   all   correct  definitions  of  any  other 
science.     The  truth  of  this  statement  is  self-evident. 

2.  While  the  sphere  here  assigned  to  the  science  possesses 
not  only  perfect  unity  and  definiteness,  but  also  exclusiveness, 
occupying  no  department  properly  pertaining  to  any  other 
science,  it  also  has  throughout  a  fixed  and  definite  relation  to 
all  the  other  sciences,  that  is,  it  is  what  the  science  of  logic 
should  be,  the  true  and  proper  antecedent  to  them  all.  It  does 
not  profess  to  teach  what  is  true  or  what  is  false,  in  any  sphere 
occupied  by  any  one  of  the  sciences ;  but  it  does  aim  to  de- 
velop those  laws  and  principles,  by  which  we  can  determine 
whether  any  given  procedure  in  the  development  of  any  of  the 
sciences,  is  or  is  not  valid  for  the  truth  of  what  is  referred 
to  in  such  process,  and  why  such  procedure  is  or  is  not  thus 
valid.  This  is  precisely  what  no  one  of  the  sciences  professes, 
or  aims,  in  any  of  its  appropriate  departments,  to  accomplish. 
Yet  what  this  science  aims  to  accomplish,  is  just  what  is 
needed,  in  all  the  sciences  alike,  in  all  intellectual  processes 
having  truth  for  their  object  and  aim.  We  certainly  need 
criteria  by  which  valid  processes  may,  in  all  cases,  be  deter- 
mined and  distinguished  from  those  which  are  not  valid. 
Hence  we  remark, 

3.  That  this  idea  when  realized  meets  a  fundamental  want  of 
universal  mind,  a  necessity  which  no  other  science  does  or  can 
meet.  The  navigator,  when  abroad  upon  the  ocean,  no  more 
needs  tables  and  instruments  by  which  he  can  determine  his 
latitude  and  longitude,  than  does  universal  mind,  educated 
mind  especially,  criteria  by  which  it  can  judge  correctly  of  the 
character  of  its  own  intellectual  processes.  Logic,  as  now  de- 
fined, aims  to  meet  this  universal  want,  and  when  realized, 
does  most  fully  and  perfectly  meet  it.     When  its  sphere  is  con- 


INTRODUCTION". 


tracted  within  narrower  limits  than  is  here  assigned  to  it,  a  fun- 
damental want  of  universal  mind  is  so  far  left  unmet,  and  that 
when  we  have  no  science,  which,  while  moving  in  its  proper 
sphere,  does  or  can  meet  that  want. 

4.  No  adequate  reason  can  be  assigned,  why  any  department 
of  the  sphere  of  this  science,  as  above  defined,  should  be  as- 
signed to  logic,  and  any  other  department  excluded  from  it. 
Nor  can  any  other  science  be  named  to  which  the  department 
excluded,  can  properly  be  assigned.  We  might,  with  the  same 
propriety,  include  the  latter  department  in  our  definition  of  the 
science  and  exclude  the  former,  as  to  include  the  former  and 
exclude  the  latter. 

5.  All  treatises,  or  most,  at  least,  attempt  to  realize  the  full 
idea  of  the  science,  as  above  defined,  though  not  nnfrequently 
in  palpable  contradiction  to  the  fixed  aim  of  the  science,  as 
previously  defined  in  such  treatises.  The  science  is  sometimes 
so  defined,  for  example,  that  the  only  fallacies  properly  falling 
under  its  cognizance,  are  those  belonging  to  one  class  exclu- 
sively, to  wit,  inferences  deduced  from  premises  whether  true 
or  false,  with  which  they  (the  premises)  have  no  logical  con- 
nection. Yet,  when  such  treatises  come  to  treat  of  fallacies, 
they  discuss  not  only  this,  but  eveiy  other  class  of  fallacies,  and 
attempt  to  give  us  universal  criteria  by  which  valid  intellectual 
processes  may  be  distinguished  from  those  which  are  not  valid, 
the  very  sphere  and  aim  of  logic,  as  above  defined.  Hence  in 
these  illogical  treatises,  fallacies  are  discussed  under  three 
classes — the  strictly  logical,  that  is,  those  which  fall  within  the 
proper  sphere  and  cognizance  of  logic,  as  defined — the  semi- 
logical,  those  which  partly  do,  and  partly  do  not,  belong  to  the 
defined  sphere  of  logic — and  the  non-logical,  those  that  logic, 
as  defined,  has  no  business  with  whatever.     It  is  just  as  wide  a 


^ffoiXS 


24  INTRODUCTION. 

departure  from  all  true  principles  of  scientific  procedure,  to 
treat  of  non-logical  fallacies,  in  a  treatise  on  logic,  as  it  would 
to  include  a  treatise  of  arithmetic  in  a  system  of  geometry. 
All  fallacies  are  really  and  truly  logical  fallacies,  or  only  a  cer- 
tain class  of  them  should  be  discussed  in  a  treatise  on  logic. 

Logic  as  distinguished  from  Esthetics. 

It  may  do  something  to  render  still  more  distinct  and  defi- 
nite our  conceptions  of  this  science  to  compare  its  sphere  and 
aim  with  those  of  another,  the  science  of  esthetics.  This  last 
has  been  commonly  defined  as  the  science  of  the  beautiful  in 
nature  and  art.  As  pertaining  to  mind,  its  appropriate  sphere 
is  t/ie  creations  of  the  imagination,  the  object  of  which  is  to 
blend  the  elements  of  thought,  not  in  harmony  with  things  as 
they  are,  but  with  the  ideas  of  beauty,  grandeur,  sublimity, 
perfection,  &c.  Esthetics,  as  a  science,  aims  to  develop  those 
laws  and  principles  in  conformity  to  which  this  faculty  must 
act,  in  order  to  realize  the  end  referred  to,  to  show  what  kind 
of  elements  must  be  blended  into  a  given  conception,  and  how 
they  must  be  blended,  so  as  to  realize  these  ideas.  Thus  it 
presents  criteria  by  which  we  can  distinguish  the  truly  beauti- 
ful from  that  which  is  not,  in  other  words,  the  valid  from  the 
invalid  procedures  of  the  imagination. 

The  true  and  proper  aim  of  the  understanding  and  judgment, 
on  the  other  hand,  is  to  blend  the  elements  of  thought  given  by 
the  primary  faculties  into  conceptions  and  judgments  in  harmo- 
ny with  things,  not  as  they  might  or  should  exist,  but  as  they 
do  exist.  Logic  aims  to  give  those  criteria  by  which  we  can 
distinguish  those  procedures  of  these  faculties  which  are  to  be 
held  as  valid  for  realities,  from  those  which  are  to  be  held  as 
not  thus  valid.    Esthetics  might,  with  some  approach  to  truth. 


INTRODUCTION.  25 

be  defined  as  the  logic  of  the  imagination,  while  logic  proper 
has  for  its  sphere  the  procedures  of  the  understanding  and 
judgment,  in  all  processes  the  aim  of  which  is  to  realize  in  pro- 
cesses of  intuition,  conception,  judgment,  and  reasoning,  the 
idea  of  truth. 

Accordance  of  the  above  conception  of  Logic  with  that  given 
by  Kant. 

The  perfect  accordance,  in  all  essential  particulars,  of  the  con- 
ception of  logic  above  developed,  with  that  given  by  Kant,  will 
appear  manifest  to  all  who  are  acquainted  with  his  treatise  on 
this  science.  To  evince  that  accordance,  we  need  only,  in  con- 
nection with  his  definition  of  the  science  above  given,  cite  the 
following  passages  from  that  treatise  :  "  In  logic  we  want  to 
know,"  he  says,  "  not  how  the  understanding  is  and  thinks,  and 
how  it  has  hitherto  proceeded  in  thinking,  but  how  it  shall  pro- 
ceed. It  is  to  teach  the  right  use  of  the  understanding,"  &c. 
Further  on,  after  giving  precisely  similar  distinctions  between 
esthetics  and  logic  that  we  have  done,  he  presents  the  following 
division  of  the  latter  science,  a  division  which  must  have  its  ex- 
clusive basis  in  a  conception  of  the  science  strictly  identical,  in 
all  essential  particulars,  if  not  in  all  others,  with  that  which  we 
have  given  :  "  We  shall  consequently  have  two  parts  of  logic  : 
the  analytic,  which  propounds  the  formal  criteria  of  truth  ;  and 
the  dialectic,  which  comprises  the  marks  and  the  rules,  by  which 
we  can  know,  that  something  does  not  agree  with  them.  In 
this  sense  the  dialectic  would  be  of  great  use  as  a  cathartic  of 
the  understanding."  He  then  goes  on  to  show  that  all  other 
conceptions  of  the  science  not  accordant  with  this  are  "im- 
proper" and  "wrong." 


26  INTRODUCTION. 

Accordance  of  the  above  idea  of  Logic  with  that  set  forth  by 
Sir  William  Hamilton. 

In  connection  with  the  fact  that  Sir  William  Hamilton  ac- 
cords in  general  with  the  conception  of  logic  as  given  by  Kant, 
the  accordance  of  the  idea  of  the  former  with  that  which  we 
have  presented  will  be  made  sufficiently  manifest  through  the 
following  paragraph  selected  from  his  article  on  Logic,  found  in 
his  Discussion  on  Philosophy  and  Literature,  p.  136,  as  pub- 
lished by  the  Harpers : 

"  We  shall  not  dwell  on  what  we  conceive  a  very  partial  con- 
ception of  the  science,  that  Dr.  Whately  makes  the  process  of 
reasoning  not  merely  its  principle,  but  even  its  adequate  object, 
those  of  simple  apprehension  and  judgment  being  considered 
not  in  themselves  as  constituent  elements  of  thought,  but  simply 
as  subordinate  to  argumentation.  In  this  view  logic  is  made 
controvertible  with  syllogistic.  This  view,  which  may  be  al- 
lowed in  so  far  as  it  applies  to  the  logic  contained  in  the  Aristo- 
telic  treatises  now  extant,  was  held  by  several  of  the  Arabian 
schoolmen  ;  borrowed  from  them  by  the  Oxford  Crackenthrope, 
it  was  adopted  by  Wallis ;  and  from  Wallis  it  passed  to  Dr. 
Whately.  But,  as  applied  to  logic,  in  its  own  nature,  this 
opinion  has  been  long  rejected,  on  grounds  superfluously  con 
elusive,  by  the  immense  majority  even  of  the  peripatetic  dia 
lecticians ;  and  not  a  single  reason  has  been  alleged  by  Dr. 
Whately  to  induce  us  to  waver  in  our  belief,  that  the  Imcs  of 
thought,  and  not  the  laws  of  reasoning,  constitute  the  adequate 
'object  of  the  science.  This  error,  which  we  cannot  now  refute, 
would,  however,  be  of  comparatively  little  consequence,  did  it 
not— as  is  notoriously  the  case,  in  Dr.  Whately 's  Elements— in- 
duce a  perfunctory  consideration  of  the  laws-  of  those  faculties 


INTRODUCTION.  27 

of  thought ;  these  being  viewed  as  only  subsidiary  to  the  pro- 
cess of  reasoning." 

The  object  of  logic,  we  repeat,  is  not  to  reveal  or  affirm  what 
is  true  or  what  is  false  in  itself,  that  being  the  exclusive  province 
of  the  various  special  departments  of  mental  operation.  Its  ex- 
clusive object,  on  the  other  hand,  is  to  develop  and  elucidate 
those  laws  of  thought  by  which  we  can  determine  whether  any 
given  intellectual  process,  whatever  its  object  may  be,  a  process 
which  professedly  reveals  and  establishes  the  truth  in  respect  to 
the  object  to  which  it  pertains,  is  or  is  not  valid  'for  its  truth, 
and  why  it  is  to  be  held  as  thus  valid  or  not  valid. 

Inadequate  and  false  conceptions  of  this  science. 

It  will  add  somewhat  to  the  distinctness  and  definiteness  of 
our  conceptions  of  this  science,  to  compare  the  conceptions 
which  we  have  set  forth,  with  certain  others  which  we  regard 
as  inadequate  or  wrong.  Among  these  the  following  only  de- 
mand special  notice. 

The  syllogistic  idea. 

The  first  which  we  adduce  is  what  may  not  inappropriately  be* 
denominated  the  syllogistic  idea,  that  which  affirms  that  the  ex- 
clusive object  of  this  science  is  to  develop  the  laws  of  reasoning, 
that  is,  to  state  what,  in  a  process  of  reasoning,  are  and  must  be 
the  relations  between  the  premises  and  conclusion,  when  the  lat- 
ter does  or  does  not  necessarily  follow  from  the  former.  A 
very  few  considerations  only  are  requisite  to  show  how  funda- 
mentally inadequate  this  idea  is  to  represent  the  true  and  ap- 
propriate sphere  of  this  science.  Take,  as  examples,  the  follow- 
ing syllogisms : 


Iso  INTRODUCTION. 

All  men  are  mortal ; 
George  is  a  man  ; 
Therefore,  he  is  mortal. 

The  conclusion,  in  this  instance,  is  not  only  true,  hut  it  results 

as  a  necessary  deduction  from  the  premises.     Take  now  another 

of  a  different  character  : 

All  mortal  beings  are  men  ; 
Every  brute  is  a  mortal  being  ; 
Therefore,  every  brute  is  a  man 

Here  we  have  a  false  conclusion.  It  has  the  same  necessary 
logical  connection  with  the  premises,  however,  that  the  conclu- 
sion of  the  former  syllogism  has.     Again  : 

All  bipeds  are  mortal ; 
All  men  are  mortal  ; 
Therefore,  all  men  are  bipeds. 

In  this  case  a  true  conclusion  is  deduced  from  premises  with 
which  it  has  no  logical  connection.     Further : 

All  mortal  beings  are  men  ; 

All  brutes  are  men  ; 

Therefore,  all  brutes  are  mortal  beings. 

Here,  also,  we  have  a  conclusion  which  is  true  in  itself,  hut 
which  is  deduced  from  premises,  hoth  of  which  are  false,  and 
with  which  it  has  no  logical  connection.     Again  : 

All  animals  are  mortal ; 
All  men  are  mortal ; 
Therefore,  all  men  are  animals. 

In  this  syllogism,  all  the  propositions  are  true ;   but  the  con- 
clusion has  no  logical  connection  with  the  premises  from  which   . 
it  is  deduced.     Once  more  : 

All  mortal  beings  are  men  ; 
George  is  a  mortal  being  ; 
Therefore,  he  is  a  man. 


INTRODUCTION. 


The  conclusion  in  this  case  is  true,  and  is  necessarily  con- 
nected with  the  premises.  Still  there  is  a  fallacy  in  the  argu- 
ment, one  premise  being  false. 

We  have  in  the  five  last  syllogisms,  five  different  kinds  of  fal- 
lacies, and  it  would  seem  that  the  science  of  logic  ought  to  give 
us  principles  by  which  we  can  determine,  in  each  case  alike, 
what  is  the  nature  and  character  of  the  fallacy,  and  why  it  is  to 
be  regarded  as  such.  Yet  with  the  first  and  last  of  the  five, 
logic,  according  to  the  present  definition,  has  nothing  whatever 
to  do.  There  being,  in  these  cases,  a  necessary  connection  be- 
tween the  premises  and  conclusion,  every  condition  required 
by  the  science  has  been  fulfilled,  and  its  mission  is  at  an  end  in 
respect  to  them.  At  the  same  time,  we  have  no  other  science 
to  which  it  pertains  to  trace  out  the  source  of  the  fallacy  in 
either  case,  and  tell  us  where  it  may  be  found,  and  why  it 
should  be  regarded  as  a  fallacy.  Numbers  three,  four,  and 
five,  only,  are  logical  fallacies,  according  to  this  definition,  and 
would  properly  be  designated  as  fallacies  in  reasoning  by  the 
science,  as  thus  defined. 

Of  the  six  syllogisms,  in  three  of  them,  numbers  one,  two, 
and  six,  the  conclusions  have  a  necessary  connection  with  the 
premises,  and  the  argument  throughout,  in  each  case,  alike 
fulfils  all  the  conditions  of  the  science,  as  now  defined :  in  the 
other  three,  though  in  the  last  two  of  them  the  intellectual  pro- 
cedure is  fundamentally  fallacious,  and  the  propositions  all  true 
in  the  first,  the  whole  of  these  syllogisms,  we  say  must  be 
classed  together  under  the  same  category  in  a  treatise  upon 
this  science,  a  treatise  developed  in  strict  consistency  with 
such  an  idea  of  its  exclusive  sphere  and  design.  Now  we 
affirm  that  logic,  when  developed  according  to  the  true  con- 
ception of  its  entire  and  proper  domain  and   adequate  aims 


30  INTRODUCTION. 

as  a  science,  will  not  thus  confound  things  which  so  fundamen- 
tally dhTer. 

In  numbers  one  and  two,  each  conclusion  has  the  same  neces- 
sary connection  with  its  premises,  yet  the  process  of  thought 
is  in  the  first  case  valid  for  the  truth  of  the  conclusion,  and  not 
valid  in  the  last.  In  the  last  four  syllogisms,  there  is.  the  same 
want  of  validity,  whether  the  conclusion  is  true  or  false.  Sup- 
pose we  ask  for  the  reason  or  grounds  of  the  difference.  To 
answer  such  an  inquiry  our  investigations  must,  in  every  case, 
take  a  Avider  range  than  the  mere  consideration  of  the  logical 
connection  between  the  premises  and  the  conclusion,  and  must 
in  all  instances  take  into  account  the  conceptions  represented  by 
the  various  terms  of  the  syllogisms,  the  judgments  represented 
in  the  propositions  of  which  the  syllogisms  are  constituted,  and 
the  connections  between  the  premises  and  the  conclusion  in  the 
same.  We  will  take  the  first  syllogism  in  illustration.  In  this 
syllogism  there  are  three  conceptions  represented  by  the  terms 
men,  mortal,  and  George.  On  examination  they  will  be  found 
to  possess  certain  fundamental  characteristics  common  to  all 
others  which  appear  in  judgments  really  and  truly  valid  for 
the  reality  and  character  of  the  objects  to  which  they  pertain, 
and  which  consequently  distinguish  all  conceptions  which  must 
be  held  as  true  from  those  which  must  not,  as  elements  of  such 
judgments,  be  thus  held.  Relations  equally  fundamental  and 
peculiar  will  be  found  to  obtain  between  the  subject  and  predi- 
cate in  each  of  the  premises  of  such  a  syllogism,  and  also  be- 
tween the  premises  themselves  and  the  conclusion  deduced 
from  them.  The  characteristics  of  the  conceptions,  on  the  one 
hand,  and  those  of  the  relations  between  the  subject  and  predi- 
cate in  each  of  the  premises,  and  between  said  premises  and  the 
conclusion  deduced  from  them,  on  the  other,  characteristics  and 


INTRODUCTION. 


relations  which  may  bo  determined  and  defined,  constitute  the 
laws  of  thought  by  which  all  valid  judgments  and  processes  of 
reasoning  may  be  distinguished  from  those  which  are  not  valid, 
inasmuch  as  all  valid  processes  do  and  must  possess  throughout 
these  identical  characteristics,  and  all  not  valid  must  be  thus 
regarded,  for  the  reason  that  they  violate  these  rules  in  seme 
particular  or  otherj  some  in  the  relations  affirmed  to  exist  be- 
tween the  premises  and  conclusion,  others,  in  those  existing  be- 
tween the  subject  and  predicate  in  one  or  the  other  of  the 
premises,  or  in  both  together,  and  others  because  they  are  con- 
stituted of  invalid  conceptions.  !N"ow  why  should  it  be  affirmed 
that  one  class  of  these  laws  of  thought  come  within  the  appro- 
priate sphere  of  logic,  and  that  either  of  the  others  should  be 
excluded  from  it  ?  No  reason  whatever  can  be  assigned  for 
such  an  assumption.  If  any  individual  should  accomplish  what 
is  needed  in  regard  to  any  one  of  these  departments,  the  rela- 
tions between  the  premises  and  conclusion  in  processes  of*  rea- 
soning, for  example,  he  would  so  far  meet  one  important  logical 
demand  of  universal  mind.  If,  when  he  has  done  thus  much, 
he  should  put  forward  the  claim,  that  he  has  occupied  the  entire 
sphere  of  the  science  of  logic,  he  would  simply  reveal  the  fact 
that  he  entertains  too  limited  conceptions  of  that  science. 

Conceptions,  judgments,  and  deductions  from  judgments  pre- 
sented as  premises,  these  together,  Ave  repeat,  constitute  the 
proper  sphere  and  object  of  this  science.  Its  object  is  to  de- 
velop and  elucidate  those  laws  of  thought  by  which  valid  con- 
ceptions, valid  judgments,  and  valid  deductions,  can  be  distin- 
guished from  those  which  are  not  valid,  and  by  which  it  can  be 
shown  in  what  respects  and  for  what  reasons  any  given  intel- 
lectual process  is  or  is  not  thus  valid. 


INTRODUCTION". 


of  Dr.  Whately  and  others. 

"  Logic  '  r.ays  Dr.  Whately,  and  we  will  give  the  definition 
in  full,  "  k,  l\<e  most  extensive  sense  which  the  name  can  with 
propriety  he  made  to  hear,  may  be  considered  as  the  science, 
and  also  as  the  art,  of  reasoning.  It  investigates  the  principles 
on  which  argumentation  is  conducted,  and  furnishes  rules  to  se- 
cure the  mind  from  error  in  its  deductions.  Its  most  appro- 
priate office,  however,  is  that  of  instituting  an  analysis  of  the 
process  of  the  mind  in  reasoning ;  and  in  this  point  of  view,  it 
is,  as  has  been  stated,  strictly  a  science/  while,  considered  in 
reference  to  the  practical  rules  above-mentioned,  it  may  be 
called  the  art  of  reasoning.  This  distinction,  as  will  hereafter 
appear,  has  been  overlooked,  or  not  clearly  pointed  out  by  most 
writers  on  the  subject ;  logic  having  been  in  general  regarded 
as  merely  an  art ;  and  its  claim  to  hold  a  place  among  the 
sciences  having  been  expressly  denied." 

*In  the  above  paragraph  there  are,  as  shown  most  indubitably 
by  Sir  William  Hamilton,  at  least  three  important  errors. 

The  first  that  we  notice  is  an  historical  one,  the  statement,  that 
logicians  have  generally  considered  logic  as  an  art,  and  not  a 
science,  whereas  in  the  language  of  the  author  just  named,  "  the 
great  majority  of  logicians  have  regarded  logic  as  a  science,  and 
expressly  denied  it  to  be  an  art.  This  is  the  oldest  as  well  as 
the  most  general  opinion." 

The  next  error  that  we  notice  pertains  to  the  nature  of  logic 
itself.  It  is  in  fact  in  no  proper  sense  an  art  of  reasoning,  its 
fundamental  aim,  as  far  as  reasoning  is  concerned,  being  not  to 
teach  us  how  to  reason,  but  to  enable  us  to  judge,  upon  scien- 
tific principles,  of  proces'ses  of  reasoning.  We  all  know  that  an 
individual  may  be  an  excellent  and  scientific  judge  of  processes 


INTRODUCTION.  33 

f  reasoning,  and  practically  a  very  bad  reasoner.     Yet  science 
nds  to  render  practice  more  perfect.     In  this  indirect  and 
secondary  sense  logic  is  an  art  of  reasoning. 

The  third  and  last  error  that  we  notice,  is  that  of  a  too  lim- 
ited and  inadequate  conception  of  the  true  sphere  and  conse- 
quent full  aim  of  the  science.  The  error  to  which  we  now  re- 
fer, consists  in  the  supposition  that  the  laws  of  reasoning,  instead 
of  the  laws  of  thought,  constitute  the  real  sphere  and  object  of 
the  science.  This  error  we  have  already  exposed  in  another 
connection.  Nothing  in  addition  is  therefore  required  on  the 
subject. 

The  idea  that  "  the  adequate  object  of  Logic  is  language?'' 

As  Dr.  Whately  proceeds  in  his  elucidation  of  what  he  re- 
gards as  the  true  and  proper  conception  of  this  science,  he  has 
fallen  into  another  important  error,  an  error  which  has  been  so 
fully  and  so  well  exposed  by  Sir  William  Hamilton,  that  we 
will  simply  present  his  statement  of  it  together  with  his  exposi- 
tion of  the  same,  without  any  additional  remarks  of  our  own  : 

"  But  Dr.  "Whately  is  not  only  ambiguous ;  he  is  contradicto- 
ry. We  have  seen  that,  in  some  places,  he  makes  the  process 
of  reasoning  the  adequate  object  of  logic ;  what  shall  we  think, 
when  we  find,  that,  in  others,  he  states  that  the  total  or  ade 
quate  object  of  logic  is  language  ?  But,  as  there  cannot  be  two 
•adequate  objects,  and  as  language  and  the  operation  of  reason- 
ing are  not  the  same,  there  is,  therefore,  a  contradiction.  '  In 
introducing,'  he  says,  '  the  mention  of  language,  previously  to 
the  definition  of  logic,  I  have  departed  from  established  prac- 
tice, in  order  that  it  may  be  clearly  understood,  that  logic  is 
entirely  conversant  about  language ;  a  truth  which  most  wri- 
ters on  the  subject,  if  indeed  they  were  fully  aware  of  it  them- 


34  INTRODUCTION. 

selves,  have  certainly  not  taken  due  care  to  impress  on  their 
readers'  (p.  56).  And  again:  'Logic  is  wholly  concerned  in 
the  use  of  language'  (p.  74). 

"  The  term  logic  (as  also  dialectic)  is  of  ambiguous  deriva- 
tion. It  may  either  be  derived  from  "koyog  (ivSia8e<ros),  reason, 
or  our  intellectual  faculties  in  general ;  or,  from  \6yog  (*  po-cpopj- 
xos),  speech  or  language,  by  which  these  are  expressed.  The 
science  of  logic  may,  in  like  manner,  be  viewed  either — 1.  As 
adequately  and  essentially  conversant  about  the  former  (the  in- 
ternal Xo'yoff,  verbum  mentale),  and  partially  and  accidentally, 
about  the  latter  (the  external  \6yog,  verbum  oris) ;  or,  2.  As 
adequately  and  essentially  conversant  about  the  latter,  partially 
and  accidentally  about  the  former. 

"  The  first  opinion  has  been  held  by  the  great  majority  of  lo- 
gicians, ancient  and  modern.  The  second,  of  which  some  traces 
may  be  found  in  the  Greek  commentators  of  Aristotle,  and  in 
the  more  ancient  Nominalists,  during  the  middle  ages  (for  the 
later  scholastic  Nominalists,  to  whom  this  doctrine  is  generally, 
but  falsely  attributed,  held  in  reality  the  former  opinion),  was 
only  fully  developed  in  modern  times  by  philosophers,  of  whom 
Hobbs  may  be  regarded  as  principal.  In  making  the  analysis 
of  the  operation  of  reasoning  the  appropriate  office  of  logic, 
Dr.  Whately  adopts  the  first  of  these  opinions ;  in  making  logic 
entirely  conversant  about  language,  he  adopts  the  second.  We 
can  hardly,  however,  believe  that  he  seriously  entertained  this 
last.  It  is  expressly  contradicted  by  Aristotle  (Analyt.  Part  i. 
10,.  §  1).  It  involves  a  psychological  hypothesis  in  regard  to 
the  absolute  dependence  of  the  mental  faculties  on  language, 
•once  and  again  refuted,  which  we  are  confident  that  Dr. 
Whately  never  could  sanction  ;  and,  finally,  it  is  at  variance 
with  sundry  passages  of  the  Elements,  where  a  doctrine  appa- 


INTRODUCTION.  So 

rently  very  ditTerent  is  advanced.  But,  be  his  doctrine  what 
it  may,  precision  and  perspicuity  are  not  the  qualities  we  should 
think  of  applying  to  it." 

General  division  of  topics. 

We  have  now  sufficiently  indicated  our  own  conception  of 
the  science  under  consideration.  The  way  has  thus  been  pre- 
pared to  enter  intelligently  upon  the  elucidation  of  the  different 
departments  of  our  subject,  which  we  shall  treat  of  under  the 
following  general  arrangement  of  topics  : 

I.  The  necessary  laws  of  thought  to  which  the  intelligence 
does  and  must  conform  in  all  valid  conceptions,  judgments,  and 
deductions,  or  processes  of  reasoning.  This  department  of  the 
science  is  denominated  by  Kant,  the  Analytic.  For  the  sake 
of  convenience  we  shall  include  what  we  have  to  say  on  this 
topic,  under  this  same  general  title. 

II.  The  doctrine  of  fallacies  which  the  philosopher  just  named 
denominates  the  Dialectic,  and  which  we  shall  attempt  to  eluci- 
date under  the  same  title. 

III.  The  doctrine  of  Method,  or  the  rules  in  conformity  to 
which  all  scientific  procedures  should  be  conducted. 

IV.  Certain  general  and  specific  applications  of  the  principles 
elucidated,  applications  adduced  for  the  purpose  of  exemplify- 
ing the  importance  of  the  science,  and  the  manner  of  applying 
its  principles. 

The  first  two  topics  embrace  the  entire  field  of  logic  consid- 
ered as  a  science.  The  last  two  are  presented  for  the  purpose 
of  elucidation. 


LOGIC. 


PART  I. 

THE     ANALYTIC. 


CHAPTER  I. 

ANALYTIC    OF    CONCEPTIONS    AND    TEEMS. 

Section  I. — Of  Conceptions. 

Conceptions  defined. 

A  conception,  or  notion,  is  a  mental  apprehension  of  some  ob- 
ject or  objects,  an  apprehension  which  we  express  by  such  terms 
as  George,  man,  tree,  plant,  animal,  &c.  Such  apprehensions 
we  represent  by  the  general  term  conception. 

Origin  and  constituent  elements  of  Conceptions. 

Knowledge,  with  the  human  intelligence,  begins  not  with 
conceptions  but  with  intuitions,  or  a  direct  and  immediate  per- 
ception of  the  reality  or  qualities  of  objects.  As  shown  in  the 
Intellectual  Philosophy,*  and  as  now  generally  admitted  by  phi- 
losophers, the  faculties  of  intuition,  or  original  perception,  are 
three, — Sense,  the  faculty  of  external  percejrtion,  the  faculty 
which  perceives  the  qualities  of  external  material  substances — 
Consciousness,  the  faculty  of  internal  perception,  the  faculty 
which  perceives  and  apprehends  the  operations  or  phenomena 
of  the  mind  itself — and  Reason,  which  apprehends  the  logical 
antecedents  of  phenomena  perceived  by  Sense  and  Conscious- 


*  A  System  of  Intellectual  Philosophy,  by  Kev.  Asa  Mahan,  j 
Barnes  &  Co. 


.  476.     New  York,  A.  8. 


ness,  to  wit,  truths  necessary  and  universal,  such  as  space,  time, 
substance,  cause,  personal  identity,  the  infinite,  &c. 

In  intuition  each  particular  quality  or  phenomenon,  together 
with  its  logical  antecedent,  is  given  singly  and  by  itself.  From 
the  nature  of  the  case,  it  cannot  be  otherwise,  the  quality  being, 
in  all  instances,  the  object  of  direct  and  immediate  perception 
or  apprehension.  By  this  we  would  not  be  understood  as  affirm- 
ing that  different  qualities  may  not  each  be  the  object  of  simul- 
taneous perception  with  others.  This  we  believe.  Yet,  as  each 
quality  is  itself  individual  and  single,  and  is  the  object  of  direct 
and  immediate  perception,  such  quality  must  be  originally  given 
singly  and  by  itself.  The  same  holds  true  of  the  logical  ante- 
cedent of  such  quality,  as  given  by  reason.  Each  quality  has 
its  special  logical  antecedent ;  and  as  the  quality  is  originally 
given  singly  and  by  itself,  the  same  must  be  held  equally  true 
of  its  logical  antecedent.  The  logical  antecedent  of  the  reality 
of  the  quality  of  extension,  for  example,  is  that  of  an  extended 
substance,  quality  necessarily  supposing  as  the  condition  of  its 
existence,  the  reality  of  substance,  it  being  impossible  to  conceive 
of  the  reality  of  the  former,  without  supposing  that  of  the  latter. 
The  same  holds  true  of  all  other  qualities,  or  phenomena,  of 
every  kind. 

The  origin  and  constituent  elements  of  conceptions  of  every 
kind  now  admit  of  a  ready  statement  and  explanation.  When 
a  quality  is  perceived,  and  its  logical  antecedent  apprehended,  we 
have  a  secondary  operation  of  the  intelligence,  an  operation  in 
which  the  apprehension  of  the  quality  and  that  of  its  logical  an- 
tecedent are  united  into  a  conception  of  a  particular  object.  As 
other  qualities  of  the  same  object  together  with  their  logical  an- 
tecedents are  perceived  and  apprehended,  they  are  blended  into 
the  same  conception,  which  thus  becomes  more  or  less  complete, 
as  it  more  or  less  fully  represents  its  object.  Thus  if  the  object 
is  material,  for  example,  a  conception  of  it  is  formed  as  a  body 
existing  in  time  and  space,  and  having  definite  extension, 
form,  color,  &c.  On  the  perception  of  subjective  phenomena, 
we  obtain,  in  a  similar  manner,  the  conception  of  mind,  as  a 
substance  possessing  the  powers  and  susceptibility  of  thought, 


ANALYTIC     OF     CONCEPTION 


feeling,  and  voluntary  determination.  All  the  elements  which 
do  or  can  enter  into  conceptions  must  be  given  by  the  primary 
faculties  referred  to,  as  these  are  the  only  original  sources  of 
cognition.  The  function  which  thus  blends  the  original  ele- 
ments of  thought  (intuitions)  into  conceptions,  is  denominated 
the  understanding ;  and  logic,  so  far  as  it  pertains  to  concep- 
tions, is  the  science  of  the  laws  of  the  understanding. 

Error  commences,  not  with  Intuitions,  but  Conceptions. 

As  intuition,  in  all  instances,  pertains  directly,  immediately, 
and  singly  to  its  respective  object,  the  fact  of  such  intuitive  per- 
ception must  always  be  held  as  valid  for  the  reality  of  its  object. 
A  denial  of  this  principle  is  a  formal  impeachment  of  the  validi- 
ty of  the  intelligence,  as  a  faculty  of  knowledge,  and  nullifies  all 
attempts  at  knowledge  of  every  kind.  All  forms  of  scientific 
procedure  also  have  their  basis  in  the  assumed  truth  of  this 
principle,  the  validity  of  intuition  for  the  reality  of  its  objects. 
Nor  can  any  reasons  be  assigned  for  the  assumption  that  any 
one  class  of*  intuitions  should  be  regarded  as  thus  valid,  and 
others  not.  No  principles,  therefore,  are  required  to  enable  us 
to  distinguish  valid  from  invalid  intuitions. 

One  universal  division  of  conceptions,  however,  is  that  of  true 
and  false.  Here  valid  and  invalid  cognitions  first  appear  in  the 
process  of  thought,  and  hence  the  necessity  of  valid  criteria  by 
which  the  one  class  may  be  distinguished  from  the  other. 

Universal  characteristics  of  all  valid  and  invalid  Conceptions. 

The  universal  characteristics  which  distinguish  all  conceptions 
which  should  be  held  as  valid  for  the  reality  and  character  of 
their  respective  objects,  from  conceptions  which  should  not  be 
thus  held,  may  now  be  very  readily  and  distinctly  pointed  out. 

1.  All  conceptions  which  embrace  those  elements  only,  which 
have  been  really  and  truly  given  by  intuition  relatively  to  any 
object,  must  be  held  as  valid  throughout  for  the  reality  and 
character  of  such  object. 


40  LOGIC. 

2.  All  conceptions  also  must  be  held  as  thus  valid  which  em- 
brace such  intuitions  exclusively,  together  with  their  necessary 
logical  antecedents.  If  the  intuition  is  thus  valid,  so  must  all 
its  necessary  logical  antecedents  and  consequents  be.  Of  this 
there  can  be  no  doubt. 

3.  All  conceptions,  on  the  other  hand,  which  embrace  any 
elements  not  thus  given  in  respect  to  the  objects  of  said  concep- 
tions, must  be  held  as  not  valid  for  such  objects. 

The  truth  of  the  above  principles  is  serf-evident.  The  only 
question  to  be  determined  is,  how  may  we  know  when  a  given 
conception  has  one  or  the  other  of  the  above  characteristics  ? 
To  accomplish  this  end  is  the  object  of  the  following  distinctions 
and  elucidations. 

Spontaneous  and  Reflective  Conceptions. 

There  are  two  states  in  which  each  conception  may  be  con- 
templated— to  wit,  as  it  first  appears  in  the  intelligence  through 
the  spontaneous  action  of  the  understanding  ;  and  as  it  appears 
when  each  element  embraced  in  it  has  been  the  qbject  of  dis- 
tinct reflection,  and  the  entire  conception,  with  all  its  constituent 
elements,  is  presented  in  consciousness  in  a  distinct  and  reflec- 
tive form.  All  the  elements  embraced  in  the  conception,  in  its 
reflective,  is  really  found  in  it  when  in  its  spontaneous  form. 
In  the  latter  state,  however,  each  element  is  given  obscurely 
and  indistinctly.  In  the  former,  in  a  form  distinct  and  well 
defined,  as  a  part  of  the  whole  conception. 

First  and  second  Conceptions. 

Another  important  distinction  between  conceptions,  a  distinc- 
tion for  which  we  are  indebted  to  Sir  William  Hamilton,  and 
which  was  first  developed,  as  b  states,  by  Arabian  philosophers, 
is  that  of  first  and  second  conceptions.  "  A  first  notion"  (con- 
ception), says  the  writer  above  named,  "  is  the  concept  of  a 
thing  as  it  exists  in  itself,  and  independent  of  any  operation  of 
thought,  as  John,  man,  animal,  &c.     A  second  notion  is  the 


ANALYTIC      OF      CONCKPTIONS 


concept,  not  of  an  object  as  it  is  in  reality,  but  of  the  mode  un- 
der which  it  is  thought  by  the  mind,  as  individual,  species,  ge- 
nus, &c.  The  former  is  the  concept  of  a  thing — real — imme- 
diate— direct ;  the  latter  is  the  concept  of  a  concept — formal — 
mediate — reflex."  In  other  words,  when  a  conception  is  contem- 
plated as  immediately  pertaining  to  its  object,  as  it  is  in  itself, 
and  that  without  reference  to  other  conceptions,  it  is  denomi- 
nated a  first  conception.  When  it  is  contemplated  in  its  rela- 
tion to  other  conceptions,  and  as  being  capable  of  being  classed 
with,  or  separated  from  them,  then  it  is  denominated  a  second 
conception.  When,  for  example,  we  contemplate  the  concep- 
tions represented  by  such  terms  as  John,  man,  animal,  &c,  not 
as  merely  pertaining  to  some  object,  or  class  of  objects,  but  in 
reference  to  the  mode  or  form  in  which  they  pertain  to  them, 
that  is,  as  individual,  species,  or  genus,  and  consequently  as  ca- 
pable of  being  classed  with  others  which  pertain,  in  a  similar 
manner,  to  their  object,  these,  we  repeat,  are  denominated 
second  conceptions.  It  is  with  conceptions  of  this  class  espe- 
cially that  logic,  as  a  science,  has  to  do.  Phenomena  must  be 
classified,  before  their  laws  can  be  determined.  So  with  con- 
ceptions. Before  the  laws  of  thought  can  be  determined, 
thought  itself  must  be  classified  by  reflection. 

Matter  and  sphere  of  Conception. 

By  the  matter  of  the  conception  is  meant,  the  intuitions  ac- 
tually included  in  it.  By  the  sphere  of  a  conception,  we  mean 
the  number  of  individuals  embraced  under  it.  The  conceptions 
represented  by  the  term  John,  for  example,  as  to  its  matter, 
represents  all  the  elements  given  by  intuition,  in  respect  to  this 
individual,  and  as  to  its  sphere,  is  limited  to  this  one  person,  it 
being  applicable  to  none  other.  The  conception  represented 
by  the  term  man,  as  to  its  ma'  »ir,  represents  all  intuitions, 
and  those  only  which  are  common  to  all  individuals  of  the 
race ;  and  as  to  its  sphere,  it  comprehends  every  such  individual. 

"  The  matter  and  sphere  of  a  conception,"  as  Kant  observes, 
"  bear  to  one  another  a  converse  relation."     The  more  elements 


42  LOGIC. 

(intuitions)  a  conception  embraces,  that  is,  the  more  it  contains 
so  far  as  its  matter  is  concerned,  the  less  number  of  individuals 
does  it  represent,  that  is,  the  narrower  is  its  sphere,  and  vice 
versa. 

The  greatness  or  narrowness  of  the  sphere  of  a  conception 
depends  upon  the  number  of  individuals  which  take  rank  un- 
der it. 

Individual,  generic  or  generical,  and  specific  or  specifical  Con- 
ceptions. 

Conceptions  which  pertain  to  individuals  are  denominated  in- 
dividual conceptions.  Those  which  pertain  to  kinds  which  em- 
brace, not  individuals  as  such,  but  sorts  or  classes  of  individuals 
(species)  under  them,  are  denominated  generic  or  generical  con- 
ceptions. Those,  on  the  other  hand,  which  pertain  to  the  sorts 
(species)  which  are  contained  under  the  generic  or  generical 
conception,  are  denominated  specific  or  specifical  conceptions. 
The  individual  conception  embraces  all  the  elements  given  by 
intuition  relatively  to  the  one  object  to  which  it  (the  concep- 
tion) pertains.  The  generic  conception  embraces  only  the  in- 
tuitions which  are  common  to  all  the  specific  conceptions  which 
rank  under  it,  and  to  all  the  individuals  which  rank  xmder  its 
various  specific  conceptions.  The  specific  conception  embraces 
all  the  elements  of  intuition  belonging  to  the  generic,  and  also 
all  that  belong  to  the  particular  class  which  it  represents,  and 
which  are  not  found  in  the  class  from  which  the  former  is  sepa- 
rated. 

.      Highest  genus  and  lowest  species. 

It  is  evident  that  a  conception  may  be  generic  relatively  to 
another  and  lower  conception,  and  itself  specifical,  relatively  to 
one  pertaining  to  a  higher  genus.  Thus  the  conception  repre- 
sented by  the  term  man,  is  generic  relatively  to  those  which 
pertain  to  different  orders  of  the  race,  and  at  the  same  time, 
specifical  relatively  to  that  of  a  higher  genus  represented  by 
such  terms  as  rational  beings,  including  as  a  genus  men,  an- 
gels, &c. 


ANALYTIC     OF     CONCEPTIONS. 


A  genus  which  is  not  a  species  is  called  the  highest  genus.  A 
species  which  is  not  a  genus,  is  called  the  lowest  species.  The 
following  remarks  of  Kant  upon  this  subject  are  worthy  of 
special  regard : 

"  If  we  conceive  of  a  series  of  several  conceptions  subordinate 
to  one  another — for  example,  iron,  metal,  body,  substance,  thing 
• — we  may  obtain  higher  and  higher  genera  ;  for  every  species  is 
always  to  be  considered  as  a  genus  with  regard  to  its  inferior 
conception.  For  instance,  the  conception  of  a  man  being  ge- 
nerical  with  regard  to  that  of  a  philosopher,  till  we  at  last  arrive 
at  a  genus  that  cannot  be  a  species  again.  And  one  of  that  sort 
we  must  finally  reach  ;  because  there  must,  at  last,  be  a  higher 
conception,  from  which,  as  such,  nothing  can  be  further  ab- 
stracted without  the  whole  conception  vanishing.  But  in  the 
whole  series  of  species  and  of  genera  there  is  no  such  thing  as 
a  lowest  conception  of  species,  under  which  no  other  conception 
or  species  is  contained  ;  because  one  of  that  sort  could  not  pos- 
sibly be  determined.  For,  if  we  have  a  conception,  which  Ave 
apply  immediately  to  individuals,  specific  distinctions,  which  we 
do  not  notice,  or  to  which  we  pay  no  attention,  may  exist  in 
respect  to  it.  There  are  no  lowest  conceptions,  but  compara- 
tively, for  use,  which  have  obtained  this  signification,  as  it  were, 
by  convention,  provided  that  we  are  agreed  not  to  go  deeper 
in  a  certain  matter. 

"  Relatively  to  the  determination  of  the  specifical  and  of  the 
generical  conception,  then,  this  universal  law — There  is  a  genus 
that  cannot  be  any  more  a  species  ;  but  there  are  no  species  but 
what  may  become  genera  again — holds  good." 

Empirical  and  national  Conceptions. 

Intuitions  are  also  classed  as  empirical  and  rational.  All  in- 
tuitions derived  through  perceptions  external  and  internal,  that 
is,  through  the  intuitions  of  sense  and  consciousness,  are  called 
empirical,  being  derived  through  experience.  Those,  on  the 
other  hand,  which  sustain  the  relation  of  logical  antecedents  to 
empirical  intuitions,  such,  for  example,  as  the  intuitions  of  space, 


44  LOGIC. 

time,  cause,  substance,  &c,  are  denominated  rational  intuitions, 
being  the  intuitions  of  that  faculty  or  function  of  the  intelligence 
denominated  the  reason. 

Now  conceptions,  the  leading  elements  of  which  are  intuitions 
of  qualities  of  substances  material  and  mental  in  the  world  with- 
in and  around  us,  qualities  which  are  the  objects  of  perception, 
external  and  internal,  are  called  empirical  conceptions.  All 
such  conceptions  are  constituted  of  two  classes  of  elements,  the 
empirical  and  rational,  that  is,  intuitions  of  sense  and  conscious- 
ness, on  the  one  hand,  and  of  reason  on  the  other,  all  such  ob- 
jects, for  example,  being  apprehended  as  substances  or  causes 
existing  in  time  and  space,  &c,  and  as  possessed  of  certian  qual- 
ities and  attributes.  The  latter  class  of  elements  are  given  by 
immediate  perceptions,  external  or  internal,  and  the  former  by 
the  reason.     Such  conceptions  are  denominated  empirical. 

When  the  rational  intuition  becomes  itself  the  object  of  re- 
flection and  abstraction,  and  the  intelligence  apprehends  its 
object  in  a  distinct  and  reflective  form,  as  it  is  in  itself,  and  in  its 
relations  to  objects  of  empirical  conceptions,  we  then  have  what 
is  denominated  rational  conceptions :  those  of  time,  as  the  place 
of  events  ;  of  space,  as  the  place  of  bodies  ;  of  substances,  as  the 
subjects  of  qualities ;  and  of  causes,  as  the  origin  of  events,  &c. 
Rational  conceptions  sustain  to  the  empirical  the  relations  of 
logical  antecedents,  the  reality  of  the  objects  of  the  latter  being 
conceivable  and  possible,  but  upon  the  condition  of  that  of  the 
objects  of  the  former  class.  Thus  the  reality  of  body  is  neither 
conceivable  nor  possible,  but  upon  the  supposition  of  the  reality 
of  space.  So  of  time  relatively  to  succession,  of  substance  rela- 
tively to  qualities,  and  of  cause  in  respect  to  events.  If  there 
is  no  space,  no  time,  no  substance,  or  causes,  there  can  be  no 
bodies,  succession,  qualities,  nor  events.  The  conceptions  of 
space,  time,  substance,  cause,"  &c,  are  therefore  denominated 
the  logical  antecedents  of  those  of  body,  succession,  qualities, 
and  events.     So  in  all  other  instances.  ' 


ANALYTIC     OF     CONCEPTIONS. 


Presentative  and  representative 

Sir  William  Hamilton  has  classed  all  our  knowledge  under 
two  divisions — that  which  is  derived  by  direct  and  immediate 
intuition  of  the  qualities  of  objects — and  that  which  pertains  to 
such  qualities  mediately,  through  the  consciousness  of  sensa- 
tions, for  example.  Qf  the  first  kind  are  our  intuitions  of  the 
primary  qualities  of  matter,  those  which  belong  to  matter  as 
such — for  example,  extension,  form,  &c.  Our  intuitions  of  the 
secondary  qualities,  such  as  taste,  smell,  and  soimd,  are  not  dir 
rect  and  immediate,  but  indirect  and  mediate,  that  is,  through 
the  consciousness  of  sensations.  Such  intuitions  are  therefore 
called  representative.  Our  intuitions  of  the  secundo-primary 
qualities,  on  the  other  hand,  those  qualities  which  distinguish 
one  class  of  material  substances  from  another,  such,  for  example, 
as  gravity,  cohesion,  &c,  are  partly  presentative  and  partly  rep- 
resentative. 

Conceptions  constituted  of  presentative  intuitions  may  be 
called  presentative  conceptions.  Those  constituted  of  the  other 
class  would  then  be  denominated  representative.  The  same 
conception  may  partake  partly  of  one,  and  partly  of  the  other 
character. 

Abstract  and  concrete  Conceptions. 

Conceptions  also  are  properly  classed  as  abstract  and  con- 
crete. The  former  pertain  to  some  single  quality  given  by  in- 
tuition, irrespective  of  the  particular  object  to  which  such  quali- 
ty belongs,  or  to  which  the  intuition  pertains — conceptions  rep- 
resented by  such  terms  as  redness,  whiteness,  roundness,  Tight- 
ness, &c. 

Concrete  conceptions  pertain  to.  their  objects  as  they  actually 
exist,  and  combine  all  the  elements  given  by  intuition  relatively 
to  such  objects — conceptions  expressed  by  such  concrete  terms 
as  George,  man,  animal,  &c. 


Positive,  privative,  and  negative  Conceptions. 

Conceptions  which  embrace  those  intuitions  only  which  are 
actually  given  by  intuition  in  respect  to  their  objects,  and  refer 
to  their  objects  as  actually  possessed  of  the  qualites  which  such 
intuitions  embrace,  are  called  positive ;  such  conceptions,  for  ex- 
ample, as  are  represented  by  such  terms  as  sound,  speech,  a 
man  speaking,  &c.  Conceptions  which  pertain  to  their  objects 
as  void  of  certain  qualities  which  might  be  supposed  to  have 
been  given  by  intuition  as  pertaining  to  the  object,  are  denomi- 
nated privative  conceptions ;  conceptions,  for  example,  ex- 
pressed by  such  terms  as  deafness,  dumbness,  a  man  silent,  &c. 
When,  on  the  other  hand,  the  conception  pertains  to  its  object, 
as  merely  void  of  certain  characteristics,  or  as  by  no  possibility 
possessed  of  them,  then  it  is  denominated  a  negative  concep- 
tion. Such  conceptions  are  represented  by  such  terms  as  a 
dumb  statue,  a  lifeless  corpse,  &c. 

Conception  classed  under  the  principle  of  unity,  plurality,  and 
totality. 

.  Every  conception  pertains  to  its  object  as  numerically  one — 
an  individual,  John ;  or  as  many — a  multitude  ;  a  number  of 
individuals — as  John,  Thomas,  Samuel,  &c. ;  or  as  a  totality,  a 
whole  of  which  each  individual  is  an  integral  part — a  troop  of 
horse,  &c.  For  this  reason  they  are  classed  under  the  catego- 
ries above  named. 

Inferior  and  superior  Conceptions. 

When  one  conception  takes  rank  as  a  species  under  another 
as  its  genus,  as,  for  example,  the  conceptions  of  the  various  spe- 
cies of  fruit-bearing  and  forest  trees  ranked  under  that  of  the 
genus  tree,  the  former  class  of  conceptions  are  denominated  in- 
ferior, and  the  latter  superior  conceptions. 

"The  inferior  conception,"  as  Kant  well  observes,  "is  not 
contained  in  the  superior,  for  it  contains  more  in  itself  than  the 


pk 


ANALYTIC     OF     COXCEPTIONS.  47 


superior,  but  is  contained  under  it,  because  the  superior  contains 
the  ground  of  the  cognition  of  the  inferior."     We  know  the  ap- 

Le-tree,  as  a  tree,  for  example,  through  the  superior  conception 

(presented  by  the  term  tree. 


Concrete  and  characteristic  Conceptions. 


We  commonly  have  two  classes  of  conceptions  relatively  to 
the  same  object, — the  one  embracing  in  concrete  all  the  ele- 
ments given  by  intuition  in  respect  to  the  object,  and  the  other 
embracing  those  only  which  peculiarize  and  distinguish  that  ob- 
ject from  all  others.  The  former  class  of  conceptions  Ave  have 
already  designated.  The  latter  may  be  denominated  charac- 
teristic conceptions.  It  is  through  this  conception  that  objects 
are  distinguished  one  from  another,  recognized  and  classified. 

Laics  of  thought  pertaining  to  the  validity  of  Conceptions. 

We  are  now  prepared  to  state  the  general  laws  of  thought 
pertaining  to  the  validity  of  conceptions.  All  conceptions,  as 
we  have  seen,  together  with  all  their  logical  antecedents  and 
consequents,  are  to  be  held  as  valid  for  their  objects — concep- 
tions which  are  constituted  of  real  intuitions  in  respect  to  such 
objects.  Just  so  far  as  any  conception  is  constituted  of  intui- 
tions not  thus  given,  it  is  not  thus  valid.  These  are  the  general 
laws.  A  conception,  we  would  further  state,  is  valid  when,  and 
only  when,  all  judgments  legitimately  deduced  from  it  are 
themselves  valid  in  respect  to  their  object.  How  often,  for  ex- 
ample, when  certain  judgments  are  expressed  in  regard  to  per- 
sons or  objects  do  we  hear  the  reply,  "You  are  totally  mis- 
taken in  your  conception  of  such  person  or  object ;"  or,  "  That 
judgment  is  based  upon  a  total  misconception  of  its  object;"  or, 
"You  are  right  in  your  conception,"  &c.  Wrong  conceptions 
lead  to  misjudgments.  Let  us  now  apply  them  to  particular 
conceptions  and  to  particular  classes  of  conceptions. 


Particular ;  general,  and  abstract  Conceptions. 

Particular  conceptions  are  valid  when,  and  only  when,  such 
conceptions  embrace  no  elements  hut  actual  intuitions,  empiri- 
cal and  rational  in  respect  to  such  objects.  Intuitions  with  all 
their  necessary  or  logical  antecedents  and  consequents,  being 
thus  valid,  the  same  must  be  true  of  conceptions  into  which 
such  intuitions  only  enter  as  constituent  elements.  This  holds 
true,  whether  the  conception  relative  to  its  object  is  complete 
or  incomplete,  that  is,  whether  it  represents  the  whole,  or  only 
a, part  of  the  qualities  of  its  object ;  for  whatever  is  necessarily 
implied  in  the  existence  of  a  quality,  must  be  true  of  all  objects 
to  which  the  quality  pertains,  and  that  whether  it  exists  in  such 
objects  in  connection  with  other  qualities  or  not. 

For  this  reason,  abstract  conceptions,  with  all  their  necessary 
antecedents  and  consequents,  must  be  valid  for  their  objects. 
General  conceptions  are  valid,  when  they  embrace  those  ele- 
ments only  which  are  common  to  every  particular  conception 
contained  under  it,  and  when  each  of  the  former  embrace  those 
elements  only  which  are  actually  given  by  intuition  relatively 
to  its  object.  This  for  reasons  above  stated  holds  true,  whether 
the  general  conception  be  complete  or  incomplete. 


Individual,  specifical,  and  <; 

What  has  been  said  of  particular,  being  applicable  in  all  re- 
spects to  all  individual  conceptions,  nothing  further  need  be 
added  in  respect  to  the  latter. 

When  individual  conceptions  ranking  under  the  specifical  are 
valid,  the  latter  are  also  valid  for  their  objects,  when  they 
embrace  all  the  elements  contained  in  the  generic,  together  with 
all  those  that  are  common  to  all  the  individual  conceptions 
which  rank  under  the  specifical.  Thus,  for  example,  the  specifi- 
cal conception  represented  by  the  term  apple-tree  is  valid, 
when  said  conception  embraces  all  the  elements  contained  in 
the  conception  represented  by  the  term  tree,  together  with  all 
those  common  to  all  valid  conceptions  pertaining  to  all  apple- 


ANALYTIC     OF     CONCEPTIONS. 


trees  of  every  kind  and  sort.     So  of  all  other  speeifical  concep- 
tions. 

Generical  conceptions  are  valid  when  they  include  those  ele- 
ments only  strictly  common  to  all  valid  speeifical  ones  contained 
under  the  former. 

Presentative  and  representative  Conceptions. 

Preventative  conceptions,  those,  for  example,  which  are  con- 
stituted of  intuitions  pertaining  to  the  primary  and  secundo- 
primary  qualities  of  matter,  must  be  valid  absolutely  for  their 
objects.  This  is  self-evident.  All  conceptions  also,  so  far  forth 
as  they  are  constituted  of  such  conceptions,  are  thus  valid. 

Representative  conceptions,  on  the  other  hand,  can,  from  the 
nature  of  the  case,  have  only  a  relative  validity.  Our  knowl- 
edge of  the  secondary  qualities  of  matter,  for  example,  is  me- 
diate, through  the  consciousness  of  sensations.  The  subjects  of 
such  qualities,  therefore,  are  known  to  us  only  as  the  otherwise 
unperceived  causes  of  such  sensations.  Our  conceptions  of 
them,  therefore,  are  valid  in  this  sense  only,  that  constituted 
as  our  sensibility  now  is,  there  is  in  sixch  objects  a  power  thus 
to  affect  us.  Our  presentative  conceptions  are  valid,  not  for 
ourselves  merely,  but  for  all  intelligents.  Our  representative 
conceptions  are  valid  only  for  beings  constituted  in  respect  to 
their  sensitivity,  as  we  are,  and  when  in  our  circumstances, 
questions  which  can  be  resolved  only  by  a  reference  to  general 
experience. 

The  same  conceptions  are  often  constituted  of  presentative 
and  representative  intuitions,  and  are,  consequently,  in  corre- 
sponding degree  absolutely  and  relatively  valid. 

Concrete  and  characteristic  Conceptions. 

Concrete  conceptions  are  valid,  when  they  are  constituted 
exclusively  of  actual  intuitions  in  respect  to  their  object,  and 
when  they  embrace  all  the  intuitions  thus  given,  and  as  given. 

Characteristic  conceptions  are  valid,  when  they  are  consfci- 


50  LOGIC. 

tuted  of  such  intuitions  of  those  qualities  which  belong  exclu- 
sively to  the  object  of  said  conceptions,  and  which  are  always 
connected  with  them.  Let  A,  for  example,  represent  some  ob- 
ject or  class  of  objects,  and  B  a  quality  which  belongs  to  no 
object  but  A,  and  is  always  present  as  a  constituent  element 
of  A.  The  conception  represented  by  the  term  B,  is  valid  as  a 
valid  characteristic  conception  of  A.  When  the  quality  repre- 
sented by  the  term  B  appears,  the  presence  of  all  that  are  rep- 
resented by  A  may  be  affirmed. 

A  conception  may  often  be  assumed  as  valid  for  ordinary 
practical  purposes,  which  should  not  be  assumed  as  the  basis  of 
any  truly  scientific  procedure. 

Inferior  and  superior  Conceptions. 

The  rules  just  stated  in  respect  to  individual,  specifical,  and 
generic  conceptions,  embrace  all  that  need  be  said  of  inferior 
and  superior  ones,  the  latter  being  only  different  forms  of  rep- 
resenting the  former. 

Empirical  and  rational  Conceptions. 

All  empirical  conceptions  fall  directly  under  the  laws  and 
rules  already  defined  and  elucidated.  We  have  occasion, 
therefore,  to  speak  only  of  the  latter  class,  those  which  sustain 
to  the  former  the  relation  of  logical  antecedents.  If  any  con- 
ception is  to  be  held  as  valid  for  its  object,  all  that  is  contained 
and  implied  in  its  logical  antecedents  must  be  regarded  as 
equally  valid  for  the  same  object.  A  fundamental  element  of 
our  conception  of  body,  for  example,  is  that  of  a  substance  con- 
tained in  space,  and  which  occupies  space.  Whatever,  there- 
fore, is  necessarily  implied  in  the  conception  of  the  latter,  must 
be  absolutely  valid  for  the  object  of  the  former  conception. 
The  same  holds  true  of  all  other  rational  intuitions.  All  the 
necessary  logical  antecedents  of  a  valid  intuition  must  be  just 
as  valid  as  the  intuition  itself  in  respect  to  the  object  of  said  in- 
tuition.    The  validity  of  the  rational  conception,  therefore,  can 


be 


ANALYTIC     OF     TERMS. 


>e  denied  but  upon  one  assumption,  the  absolute  objective  in- 
validity of  all  empirical  conceptions,  together  with  that  of  the 
intuitions  of  which  the  former  are  constituted.  This  would  be 
an  utter  and  universal  impeachment  of  the  intelligence  itself, 
as  a  faculty  of  knowledge,  and  would  annihilate  the  validity  of 
the  impeachment  itself. 

All  conceptions  conforming  to  the  principles  above  defined 
are  to  be  held  as  valid.  All  violations,  in  whole  or  in  part,  of  any 
of  those  principles  are  to  be  held  as  in  a  corresponding  degree 
invalid.  How  conceptions  became  thus  vitiated,  it  will  be  our 
object  to  show,  when  we  come  to  the  Dialectic,  the  invTestiga* 
tion  of  the  sources  of  fallacy. 


Section  II. — Of  Teems. 

Very  little  is  requisite  in  regard  to  the  subject  of  the  present 
section,  to  wit,  terms.  In  logic  a  conception,  or  notion,  ex- 
pressed in  language  is  called  a  term.  All  that  is  employed  for 
this  purpose,  that  is,  to  represent  the  conception,  is  included  in 
this  definition. 

It  is  evident  from  the  above  definition,  that  a  term  may  con- 
sist of  one,  or  many  words ;  as,  man,  or  a  man  on  horseback, 
a  horseman,  or  a  troop  of  horse,  &c. 

Singular  and  common  Terms. — Significatss. 

In  the  science  of  logic,  terms  are  divided  into  two  classes, 
singular  and  common.  All  terms  which  represent  individuals, 
or  single  objects  only,  are  called  singular  terms,  as  George,  the 
Hudson,  New  York,  &c.  Those,  on  the  other  hand,  which 
represent  classes  of  individuals,  as  man,  river,  mountain,  &c, 
are  called  common  terms.  The  individuals  which  a  common 
term  represents  are  denominated  its  significates. 

Relations  of  Logic  to  Terms. 

Logic  has  to  do  with  terms  only  indirectly,  that  is,  as  the 
representatives  of  conceptions.     What  is  required  in  regard  to 


the  term  is,  that,  according  to  its  received  import,  it  shall  fully 
and  distinctly  represent  its  conception,  and  nothing  more  nor 
less.  It  must  not,  according  to  received  usage,  represent  more 
nor  less  elements  than  are  included  in  the  conception ;  for,  in 
such  cases  wrong,  and  not  the  right  conceptions  are  represented. 


CHAPTER  II. 

OF    JUDGMENTS. 

Section  I. — Of  Judgments  considered  as  Mental  States. 

A  judgment  is  an  intellectual  apprehension  in  which  a  certain 
relation  is  mentally  affirmed  to  exist  between  two  or  more  con- 
ceptions. We  have  in  our  mind,  for  example,  the  conception 
of  body  and  space.  On  reflection,  we  perceive  a  necessary  re- 
lation between  them,  or  rather  between  their  oHjects.ia  relation 
of  this  character,  to  wit :  the  existence  of  the  K>rmer|can  be 
conceived  of  as  possible,  but  upon  one  condition,  the  admission 
of  the  reality  of  the  latter.  The  mind  then  becomes  distinctly 
conscious  of  the  truth,  that  body  supposes  space.  This  mental 
affirmation  is  a  judgment.  We  have  in  our  minds  also  the  con- 
ceptions represented  by  the  terms  man,  on  the  one  hand,  and 
mortal,  on  the  other ;  we  perceive  that,  as  a  matter  of  fact,  all 
that  is  included  in  the  latter  conception,  holds  true  of  every  in- 
dividual represented  by  the  former.  Mortality  is,  therefore, 
mentally  affirmed  of  all  men.  This  mental  affirmation,  also,  is 
a  judgment.  So  in  all  other  instances.  Whenever  a  certain  re- 
lation is  affirmed  to  exist  between  two  or  more  conceptions,  or 
between  the  objects  of  the  same,  this  mental  affirmation  is  a 
judgment. 

Matter  and  form  of  Judgments. 

Logic,  as  a  science,  as  we  have  seen,  pertains  not  at  all  di- 
rectly to  the  particular  objects  about  which  the  thoughts  are 


JUDGMENTS.  53 


employed  in  particular  conceptions,  judgments,  and  reasonings, 
but  to  the  laws  of  thought  itself  relating  to  such  objects.  So  it 
distinguishes  between  the  matter  and  form  of  judgments,  and 
takes  cognizance  directly  only  of  the  latter.  The  former  con- 
sists of  the  special  notions  or  judgments  relating  to  their  par- 
ticular objects,  one  judgment  pertaining  to  one  object,  or  class 
of  objects,  and  another  to  another.  The  latter,  the  form  of  the 
judgment,  pertains  to  its  character  relative  to  other  judgments, 
as  affirmative  or  negative,  universal  or  particular,  &c. 

Logic,  as  a  science,  considers  specially  the  form  of  the  judg- 
ment, and  has  to  do  with  the  matter  thereof,  only  so  far  as  to 
give  the  universal  criteria,  by  which  valid  may  be  distinguished 
from  invalid  judgments. 

Quantity  of  Judgment,  universal,  particular,   individual  or 
singular. 

When  judgments  are  contemplated  relatively  to  the  num- 
ber of  objects  of  the  class  to  which  they  pertain,  the  number 
which  is  embraced  in  the  judgment,  we  then  refer  to  the  quan- 
tity of  judgments,  as  whether  the  relation  affirmed  is  conceived 
of  as  holding  true  of  all  such  objects,  or  of  a  part  of  them,  or 
of  some  one  individual.  Relatively  to  quantity,  judgments  are 
accordingly  classed  as  universal,  particidar,  and  individual,  as 
in  the  case  of  those  represented  by  the  propositions,  "  All  men 
are  mortal ;  Some  men  are  mortal ;  and,  George  is  mortal."  In 
the  first  case,  as  the  relation  is  affirmed  to  hold  true  universally 
of  all  individuals  represented  by  the  term  man,  the  judgment  is 
called  universal.  In  the  second  case,  this  relation  is  affirmed 
relatively  to  a  part  only  of  the  individuals  represented  by  this 
term.  The  judgment  is  accordingly  called  particular.  In  the 
last  case,  the  relation  is  affirmed  of  one  individual  only.  The 
judgment  is  therefore  denominated  individual.  All  judgments, 
as  far  as  the  relation  of  quantity  is  concerned,  may  be  ranked 
as  universal,  particular,  or  individual. 

According  to  Kant,  particular  judgments  might  more  prop- 
erly be  called  plurative,  because  they  relate  to  more  than  one 


individual.  In  this  he  is  no  doubt  correct,  and  equally  correct, 
while  he  expresses  such  preference,  in  adhering  to  common  usage. 
Individual  judgments  also  are,  in  logic,  treated  practically  as 
universal  ones,  because  in  the  former,  equally  as  in  the  latter, 
the  relation  affirmed  holds  in  regard  to  the  whole  subject  with- 
out exception. 

Quality  of  Judgments,  affirmative,  negative,  indefinite. 

As  far  as  quality  is  concerned,  their  own  intrinsic  characteris- 
tics, judgments  are  classed,  as  affirmative,  negative,  and  indefi- 
nite. When  one  conception  (the  subject)  is  thought  of  as  coming 
under  the  sphere  of  another  (the  predicate),  as  in  the  judgment, 
"  All  men  are  mortal,"  all  men  being  in  the  judgment  placed 
in  the  sphere,  or  class  of  mortal  beings,  the  judgment  is  called 
affirmative.  When  one  conception  is  thought  of  as  excluded 
from  the  sphere  of  another  conception,  as  in  the  judgment, 
"  Mind  is  not  matter,"  the  former  substance  being  thought  of  as 
excluded  from  the  sphere  or  class  of  material  substances,  the 
judgment  in  that  case  is  called  negative.  When,  on  the  other 
hand,  a  conception  is  thought  of  not  only  as  excluded  from  the 
sphere  of  another  conception,  but  as  included  indefinitely  in 
one  excluded  from  the  latter,  we  then  have  what  is  called  an  in- 
definite judgment.  Thus  in  the  judgment,  "  The  human  soul  is 
not  mortal,"  we  separate  the  subject  from  the  sphere  or  class  of 
mortal  beings,  and  place  it,  but  indefinitely,  in  a  class  excluded 
from  the  former,  that  is,  among  immortal  beings.  The  distinc- 
tion between  negative  and  indefinite  judgments  is  important  to 
a  correct  understanding  of  the  notion  of  judgments  themselves. 
In  logic,  however,  both  are  included  under  one,  the  negative, 
and  all  judgments  are  classed  as  affirmative  or  negative. 

Relation  of  Judgments,  categorical,  hypothetical,  and  disjunc- 
tive. 

When  one  conception  is  directly  affirmed  or  denied  of 
another,  as  in  the  judgments,  "All  men  are  mortal,  and,  the 
soul  is  not  mortal,"  the  judgment  is  denominated  categorical. 


Wl 


JUDGME X  T  S . 


hen  conceptions  are  thought  of  in  respect  to  one  another  in 
the  relation  of  antecedent  and  consequent,  as  in  the  judgment, 
"If  Caesar  was  a  usurper,  he  deserved  death,"  the  judgment  is 
then  denominated  hypothetical. 

When  a  conception  is  thought  of  as  included  hi  one  member 
of  a  certain  division,  as  in  the  judgment,  "  Caesar  was  a  hero  or 
a  usurper,"  "A  is  in  B,  C,  or  D,"  the  judgment  is  called  dis- 
junctive. From  the  nature  of  the  relation  of  the  subject  and 
predicate  in  judgments,  all  judgments  must  be  either  categori- 
cal, hypothetical,  or  disjunctive. 

REMARKS  ON  THESE  JUDGMENTS. 

Categorical  Judgments. 

In  categorical  judgments,  as  Kant  remarks,  "the  subject  and 
the  predicate  make  up  the  matter  of  the  judgment ;  the  form, 
by  which  the  relation  (of  agreement  or  disagreement)  between 
the  subject  and  predicate  is  determined  and  expressed,  is  the 
Copula,"  which,  when  expressed  in  language,  is  always — is,  or  is 
not.  Categorical  judgments,  as  Kant  further  remarks,  "  make 
up  the  matter  of  other  judgments."  With  the  following  remark 
of  this  great  logician  we  cannot  agree  :  "  But  from  this  we  must 
not  think,  as  several  logicians  do,  that  hypothetical  and  disjunc- 
tive judgments  are  nothing  more  than  different  dresses  of  cate- 
gorical ones,  and  can  therefore  be  all  reduced  to  them.  All 
the  three  judgments  depend  upon  essentially  distinct  logical 
functions  of  the  understanding,  and  consequently  must  be  dis- 
cussed according  to  their  specific  distinction."  On  a  careful 
analysis  of  any  hypothetical  judgments,  it  will  be  found,  that, 
in  all  cases,  it  is,  as  stated  in  the  Intellectual  Philosophy,  a 
universal  proposition  expressed  in  the  form  of  a  particular. 
The  proposition,  for  example,  if  Caesar  was  a 'usurper  he  de- 
served death,  is  nothing  more  than  the  universal  proposition, 
"  All  usurpers  deserve  death,"  expressed  in  a  concrete  and  par- 
ticular form.  A  comparison  of  categorical  and  hypothetical 
syllogisms  will  also  show  that  they  are  only  different  forms  of 
the  same  thing.     For  example  : 


All  usurpers  deserve  death  ; 
Caesar  was  a  usurper  ; 
Therefore,  he  deserved  death. 

rIf  Caesar  was  a  usurper,  he  deserved  death  ; 
He  was  a  usurper  ; 
Therefore,  he  deserved  death. 

The  same  may  be  shown  to  hold  true  in  all  the  forms  which 
hypothetical  judgments  assume,  and  in  regard  to  all  the  princi- 
ples and  laws  pertaining  to  hypothetical  syllogisms.  Through- 
out they  are  nothing  but  categorical  judgments,  or  syllogisms 
stated  in  a  particular  form.  , 

What  has  been  said  in  regard  to  hypothetical  judgments  be- 
ing so  directly  and  manifestly  applicable  to  the  disjunctive, 
nothing  in  addition  is  required  to  show  that  this  class  also  dif- 
fers only  in  form  from  the  categorical. 

Hypothetical  Judgments. 

In  the  language  of  Kant,  "the  matter  of  these  consists  of  two 
judgments,  which  are  connected  together  as  antecedent  and 
consequent.  The  one  of  these  judgments  which  contains  the 
ground"  (the  subject  of  the  universal  categorical)  "  is  the  ante- 
cedent ;  the  other,  which  stands  in  the  relation  of  consequence 
to  that"  (that  is,  the  predicate  of  the  universal  categorical  judg- 
ment), "the  consequent."  The  connection  affirmed  to  exist  be- 
tween them  is  denominated  the  consequence.  The  antecedent 
and  consequent  in  a  hypothetical  judgment,  answer  to  the  sub- 
ject and  predicate  in  the  categorical,  and  the  consequence  in  the 
former  to  the  copula  in  the  latter.  A  few  passing  remarks  are 
deemed  requisite  on  the  following  paragraph  from  Kant : 

"  Some  think  it  easy  to  transform  a  hypothetical  proposition 
to  a  categorical.  But  it  is  not  practicable  ;  because  they  are 
quite  distinct  in  their  very  nature.  In  categorical  judgments 
nothing  is  problematical,  but  every  thing  assertive  ;  whereas  in 
hypothetical  ones,  the  consequence  is  only  assertive  or  positive. 
In  the  latter  we  may  therefore  connect  two  false  judgments 
together,  for  in  this  case  the  whole  affair  is  the  rightnes?  in  the 


C01 


JUDGMENTS. 


nmcction — the  form  of  the  consequence  ;  upon  which  the  logi 
cal  truth  of  these  judgments  depends.  There  is  an  essential  dis 
tinction  between  these  two  propositions  :  '  All  bodies  are  divisi 
ble,  and,  if  all  bodies  are  composed,  they  are  divisible.'  In  tl» 
former,  the  thing  is  maintained  directly :  in  the  latter  it  is  main 
tained  on  a  problematically  expressed  condition  only." 

In  reply,  we  remark  : 

1.  That  while  it  is  true  that  "in  categorical  judgments 
nothing  is  problematical,  but  every  thing  assertive,  whereas 
in  hypothetical  ones,  the  consequence  only  is  assertive,"  it  is 
equally  true,  that  in  both  the  same  thing  is  asserted,  only  in 
different  forms.  This  is  manifest,  from  the  fact,  that  in  all  hy- 
pothetical syllogisms,  a  categorical  may  be  substituted  for  the 
hypothetical  judgment  (premise),  and  the  argument  will  stand 
just  as  it  did  before.     This  we  shall  see  hereafter. 

2.  Even  in  those  hypothetical  judgments  which  contain  "  two 
false  judgments,"  with  the  connection  of  necessary  consequence 
between  them,  a  universally  valid  categorical  judgment  is  al- 
ways given — a  judgment  which  alone  renders  valid  the  relation 
of  consequence  referred  to.  In  the  judgment,  for  example,  "If 
Washington  was  a  traitor  to  his  country,  he  deserved  death," 
we  have  the  two  false  judgments,  and  the  relation  of  necessary 
consequence,  under  consideration.  In  this  very  judgment, 
however,  we  have,  in  reality,  the  universal  categorical  one,  "  All 
traitors  to  their  country  deserve  death,"  and  upon  the  validity 
of  this  last  judgment  depends  that  of  the  consequence  before 
us.     The  same  holds  true  in  all  other  instances. 

3.  The  reason  why  there  is  "  an  essential  distinction  between, 
these  two  propositions,  all  bodies  are  divisible,  and,  if  all  bodies 
are  composed  they  are  divisible,"  is  not,  as  Kant  affirms,  because 
a  hypothetical  proposition  cannot  be  transformed  into  a  cate- 
gorical one,  but  because  the  two  propositions  before  us  do  not 
in  fact  belong  to  the  same  class.  The  judgment,  therefore,  "  If 
all  bodies  are  composed  they  are  divisible,"  cannot  be  trans- 
formed into  this,  "All  bodies  are  divisible."  The  former  judg- 
ment, however,  may  be  transformed  into  this,  "  All  substances 
which  are  composed  (compounded)  :m>  divisible,"  because  that, 


hi  these  instances,  what  is  affirmed  in  one  case  categorically,  is 
affirmed  in  the  other  hypothetically.  The  examples  adduced 
by  our  author  lay  no  valid  basis  for  the  conclusion  which  he  de- 
duces from  them. 

Disjunctive  Judgments. 

A  disjunctive  judgment,  is  distinguished  from  all  others  by 
this  peculiarity,  to  wit :  it  is  constituted  of  a  certain  number  of 
problematical  judgments,  all  of  which  together  sustain  such  a 
relation  to  a  certain  judgment  known  to  be  true,  that  the  object 
of  this  judgment  must  be  in  one  of  the  numbers  referred  to,  to 
the  exclusion  of  all  the  rest.  For  example,  the  judgment,  which 
all  will  admit  cannot  but  be  true,  that  the  final  determining 
cause  of  the  facts  of  the  universe  in  creation  and  providence,  is 
either  an  inhering  law  of  nature,  or  some  power  out  of  and 
above  nature,  has  its  basis  in  the  judgment  which  also  must  be 
true,  that  for  the  facts  named  some  ultimate  reason  or  cause 
must  exist.  A  is  known  to  exist.  But  it  sustains  such  relations 
to  B,  C,  and  D,  that  it  must  be  found  in  one  of  them,  to  the  ex- 
clusion of  all  the  rest.  Hence  the  disjunctive  judgment.  A  is 
in  B,  C,  or  D.  The  same  principle  obtains  in  all  disjunctive 
judgments. 

The  several  problematical  judgments  constitute  the  matter  of 
the  disjunctive  judgments,  and  are  called,  as  Kant  observes, 
"  members  of  the  disjunction  or  opposition."  Their  mutual  re- 
lations of  disjunction  or  opposition,  that  is,  the  fact  that  each 
sustains  such  relations  to  all  the  others,  that  if  it  is  true,  they 
must  be  false,  and  if  any  of  the  others  be  true,  each  of  the  rest 
must  be  false,  constitute  the  form  of  such  judgments. 

Modality  of  Judgments,  problematical,  assertative,  contingent, 
necessary  (appodictical). 

When  the  connection  between  conceptions  is  conceived  of  as 
possible,  that  is,  Math  the  conviction  that  the  relation  may  or 
may  not  exist,  as  in  the  proposition,  "  A  may  be  in  B,"  the  judg- 


JUDGMENTS.  59 

ment  is  called  problematical.  When  the  connection  is  con- 
ceived of  as  not  only  possible,  but  as  actual,  the  judgment  is 
called  assertative.  When  the  relation  is  conceived  as  actual, 
with  the  conviction  that  the  facts  might  possibly  have  been 
otherwise,  the  judgment  is  denominated  contingent ;  as  in  the 
proposition,  "A  died  on  yesterday,"  it  being  possible  to  conceive, 
while  it  is  asserted,  that  he  did  die,  at  the  time  named,  that  he 
is  yet  alive,  or  that  he  died  at  some  other  time.  When  a  rela- 
tion between  conceptions  is  conceived  of  as  not  only  actual,  but 
the  conception  is  accompanied  with  the  conviction  that  the  facts 
can,  by  no  possibility,  be  otherwise  than  they  are,  the  judgment 
is  said  to  be  necessary  or  appodictical,  as  in  the  judgment, 
"  Body  supposes  space,  or  an  event,  a  cause."  The  contradic- 
tory of  the  problematical  is  the  impossible,  a  relation  which 
cannot  be  conceived  of  as  existing. 

Remarks. 

1.  A  judgment  maybe  deemed  necessary  for  either  of  two 
reasons — the  nature  of  the  relations  between  the  conceptions,  or 
the  nature  of  the  evidence  in  favor  of  the  actual  existence  of 
such  relations.  Of  the  first  class  are  the  judgments,  "  Every 
event  has  a  cause,"  "  Two  straight  lines  cannot  inclose  a  space," 
&c.  Of  the  second,  is  the  judgment,  "That  the  square  of  the 
hypothenuse  of  a  right-angled  triangle  is  equal  to  the  sum  of 
the  square  of  its  two  sides."  Judgments  of  the  former  class 
are  called  primitive,  those  of  the  latter,  derivative. 

2.  An  assertative  judgment,  while,  from  the  nature  of  the  re- 
lations between  the  conceptions  themselves,  it  may  be,  and  is 
contingent,  may,  relatively  to  the  evidence  of  the  existence  of 
the  relations  referred  to,  be  necessary.  The  judgments,  "  The 
world  exists,  and  I  exist,"  are  of  this  character.  Relatively  to 
the  nature  of  the  relations  between  the  subject  and  predicate  in 
each  of  these  judgments,  the  judgments  themselves  are  merely 
assertative  or  contingent.  Relatively  to  the  nature  of  the  affir- 
mations of  perception  and  consciousness,  we  say  that  these  judg- 
ments must  be  true. 


60  LOGIC. 

3.  A  judgment  necessary,  from  the  nature  of  the  relations 
between  the  subject  and  predicate,  is  necessary  in  the  absolute 
sense — the  judgments,  for  example,  "  Body  supposes  space ;  and 
succession  time,"  &c.  A  judgment  necessary  relatively  to  the 
perceptions  of  sense  and  consciousness,  is  said  to  be  relatimly 
necessary ;  as,  for  example,  "  Phenomenon  supposes  substance." 
A  necessary  form  of  this  judgment  is  this :  "  Substances  are  aa 
their  phenomena."  The  logical  antecedent  of  the  phenomenon 
of  extension  is  the  reality  of  an  extended  substance  (body). 
The  logical  antecedent  of  the  subjective  phenomena  of  thought, 
feeling,  and  voluntary  determination,  is  the  reality  of  the  self  aa 
possessed  of  the  powers  of  intelligence,  sensibility,  and  will. 
The  above-named  phenomena  being  given,  the  judgments, 
"  Body  is,  and  Self  exists,"  are  necessary,  relatively  so. 

4.  Assertative  judgments,  like  the  appodictical,  are  divided 
into  two  classes — primitive  and  derivative.  The  judgments, 
"  Body  is,  and  Self  exists,"  are  of  the  first  class.  The  judgment, 
"  All  bodies  attract  each  other  directly,  as  their  matter,  and  in- 
versely as  the  squares  of  their  mean  distances,"  is  of  the  latter 
character. 

5.  All  derivative  judgments,  as  originally  given,  are  prob- 
lematical, and  subsequently  become  assertative  or  appodictical, 
as  the  case  may  be ;  that  is,  they  are  originally  given  as  possibly 
true  or  false,  and  consequently  as  capable  of  proof,  and  as  Avant- 
ing  it. 

Theoretical  and  practical  Judgments. 

Theoretical  judgments  affirm  what  does  .and  what  does  not 
really  belong  to  their  objects.  Practical  judgments,  on  the 
other  hand,  express  those  forms  or  rules  of  action  by  which  cer- 
tain ends  may  be  obtained,  or  those  actions  which  ought  or 
ought  not  to  be  performed. 

Practical  principles  are  treated  as  theoretical  ones,  when  the 
question  to  be  argued  is,  whether  the  former  are,  in  reality, 
what  they  are  judged  to  be.  As  thus  contemplated  only, 
would  logic  have  to  do  with  them. 


JUDGMENTS. 


Demonstrable,  and  indemonstrable  or  intuitive  Judgments. 

A  demonstrable  judgment  is  a  problematical  one,  of  the  class 
which  is  capable  of  being  proved.  Indemonstrable  (intuitive) 
judgments  are  those  which  are  immediately  certain,  and  for  this 
reason,  incajjable  of  proof. 

Judgments  of  the  latter  class,  since  every  intellectual  process 
properly  denominated  reasoning  commences  with  them,  are 
sometimes,  and  Avith  unquestionable  propriety,  denominated 
primitive  judgments.  Those  of  the  former,  being  in  fact  de- 
duced from  and  evinced  by  the  latter,  are  called  derivative 
judgments. 

Intuitive  judgments  by  which  the  demonstrable  may  be 
evinced,  but  which  cannot  be  subordinated  to  others,  are  called 
elemental  judgments,  and  also  principles,  a  principle  in  science 
being  always  a  judgment  which  is  itself  immediately  certain, 
and  consequently  not  evincible  through  any  other  judgment. 

A  demonstrable  judgment,  when  evinced,  may  become  a 
principle  relative  to  other  demonstrable  judgments ;  and  a  judg- 
ment which  is  derivative  in  one  science,  may  be  an  elemental 
principle  in  another. 

Analytical  and  synthetical  Judgments. 

Those  judgments  whose  certainty  is  immediately  evinced 
from  an  analysis  of,  or  reflection  on  the  conceptions  constituting 
the  subject  and  predicate  of  said  judgments,  are  called  analyti- 
cal judgments  ;  those  judgments  which  are  evincible  only 
through  other  and  more  elementary  ones,  are  called  syntheti- 
cal judgments. 

On  examination  it  will  be  found  that  all  analytical  judg- 
ments, that  is,  all  judgments  whose  validity  is  immediately  cer- 
tain, divide  themselves  into  two  classes,  and  are  and  must  be 
all  comprehended  in  one  or  the  other  of  them.  1.  Those  in 
which  the  predicate  represents  an  essential  quality  of  the  sub- 
ject, as  in  the  judgment,  "  All  bodies  have  extension."  It  is 
impossible  for  us  to  conceive  of  a  body  which  has  not  exten- 


62  LOGIC. 

sion.  In  the  judgment  before  us,  then,  the  predicate,  exten- 
sion, represents  a  fundamental  element  of  our  necessary  concep- 
tion of  body.  The  judgment  has,  and  must  have,  immediate 
certainty,  of  course.  The  same  holds  true  in  all  similar  judg- 
ments. 2.  Those  in  which  the  conception  represented  by  the 
predicate,  sustains  to  that  represented  by  the  subject,  the  rela- 
tion of  logical  antecedent,  that  is,  when  the  reality  of  the  object 
of  the  latter  conception  can  be  admitted  but  upon  the  supposi- 
tion of  that  of  the  former.  Of  this  kind  is  the  judgment, 
"Body  supposes  space."  The  reality  of  the  object  represented 
by  the  term  body,  can  be  admitted  but  upon  the  condition  of 
admitting  that  of  the  object  of  the  conception  represented  by 
the  term  spaca  So  of  the  judgments  expressed  by  such  propo- 
sitions as  "  Succession  supposes  time ;  events  a  cause ;  phe- 
nomena substance,"  &c.  All  judgments  of  this  character  can 
but  have,  of  themselves,  immediate  intuitive  certainty. 

Now  if  we  adduce  any  known  indemonstrable  judgment 
which  has  immediate  certainty,  we  shall  find,  on  examination, 
that  it  does,  in  fact,  belong  to  one  or  the  other  of  these  classes, 
and  that  this  is  the  exclusive  ground  of  its  certainty.  Take,  as 
an  illustration,  the  axiom,  "Things  equal  to  the  same  things  are 
equal  to  one  another."  On  reflection,  it  will  be  perceived,  that 
the  relation  of  equality  among  themselves,  is  the  necessary 
condition  of  their  being  equal  to  the  same  things.  In  other 
words,  the  conception  represented  by  the  words,  "  equal  to  one 
another"  (the  predicate),  is  the  logical  antecedent  of  that  rep- 
resented by  the  words,  "  things  equal  to  the  same  things"  (the 
subject).  Thus  we  might  take  up  all  similar  judgments,  and 
all  other  self-evident  ones,  and  show  that  they  do,  in  fact,  be- 
long to  one  or  the  other  of  the  classes  above  elucidated. 

Nor  is  it  possible  for  us  to  conceive  of  any  other  grounds  of 
the  immediate  certainty  of  judgments.  In  any  other  conceiva- 
ble or  definable  case,  the  relation  between  the  subject  and 
predicate  of  the  judgment  would  be  such  that  the  judgment 
would  be,  at  the  utmost,  only  problematical. 


JUDGMENTS.  63 

Criteria  of  all  first  Truths. 

"We  have,  then,  in  the  relations  before  us,  the  fundamental 
and  universal  criteria  by  which  first  truths  may  be  distin- 
guished from  all  others.  In  all  such  judgments  (first  truths) 
the  conception  constituting  the  predicate  either  exclusively 
represents  elements  contained  in  that  represented  by  the  sub- 
ject, or  the  former  conception  sustains  to  the  latter  the  relation 
of  logical  antecedent.  There  are,  and  can  be,  no  other  first 
truths  but  these.  The  criteria  of  such  truths  commonly  given, 
are  rather  external  and  circumstantial  than  intrinsically  charac- 
teristic, as  all  scientific  criteria  should  be.  We  refer  to  those 
criteria  given  by  Dr.  Reid,  and  concui-red  in  by  philosophers 
generally,  such,  for  example,  as  the  fact,  that  all  men  admit 
them  as  a  matter  of  fact  in  all  their  reasoning  ;  that  even  those 
who  deny  their  validity  act  upon  them ;  and  if  denied,  the  va- 
lidity of  all  reasoning  fails. 

Kant's  definition  of  analytical  and  synthetical  Judgments. 

According  to  Kant,  we  have  but  one  class  of  analytical  judg- 
ments, those  in  which  the  relation  of  identity  referred  to  ob- 
tains between  the  predicate  and  subject.  The  other  class  he 
represents  as  synthetical  judgments,  which,  according  to  him, 
embrace  all  judgments  in  which  all  the  elements  of  the  concep- 
tion represented  by  the  predicate  are  not  embraced  in  that  rep- 
resented by  the  subject.  He  accordingly  divides  synthetical 
judgments  into  two  classes,  the  intuitive  and  problematical, 
though  he  gives  us  no  explanations  of  the  reasons  why  one 
class  is  intuitive  and  the  other  not.  In  the  Intellectual  Phi- 
losophy, pp.  336-341,  we  have  stated  our  objections  to  our  au- 
thor's definition  of  these  two  classes  of  judgments,  the  analyti- 
cal and  synthetical,  and  to  the  use  which  he  has  made  of  the 
latter.  In  this  connection,  we  would  simply  add,  that  while 
our  definition  is  just  as  plain,  and  of  as  ready  application,  as 
that  of  Kant,  it  presents  a  much  more  simple  and  easily  un- 
derstood   classification  of  judgments.      If  any  one,  however, 


IUFI7BESITT 


64  LOGIC. 

should  prefer  the  definition  of  that  philosopher,  we  would  re- 
mind him,  that  in  that  case,  he  must  divide  synthetical  judg- 
ments into  two  classes :  those  in  which  the  conception  repre- 
sented by  the  predicate  is,  and  those  in  which  it  is  not,  the 
logical  antecedent  of  that  represented  by  the  subject,  and  that 
the  former  class,  together  with  Kant's  analytical  judgments,  are 
to  be  ranked  together,  as  first  truths,  and  that  no  other  judg- 
ments can  be  classed  with  them,  as  such  truths.  The  logical 
and  scientific  bearings  of  each  classification  will  then"  be,  in 
all  respects,  the  same,  and  nothing  but  a  verbal   difference 


Tautological,  identical,  and  implied  Judgments. 

A  tautological  judgment  is  one  in  which  the  subject  and 
predicate  are  identical,  either  in  fact  and  in  form  ;  as,  "  John  is 
John,  Man  is  man,"  &c. ;  or,  in  all  respects,  in  meaning,  so  that 
the  predicate  is,  in  no  respect,  even  explicative  of  the  subject ; 
as,  "  Man  is  a  human  being,"  &c.  Such  judgments  are  of  no 
use  whatever. 

Identical  judgments,  as  distinguished  from  tautological,  are 
those  in  which,  while  there  is  an  identity  in  fact,  there  is  such 
a  diversity  in  form  between  the  subject  and  predicate,  that  the 
latter  is  really  and  truly  explicative  of  the  former.  Of  this  char- 
acter are  all  correct  definitions ;  as,  for  example,  a  triangle  is  a 
figure  bounded  by  three  straight  lines.  Of  the  same  character 
is  the  class  of  analytical  judgments;  in  which  the  predicate  rep- 
resents some  element  or  quality  of  the  subject;  as,  "All  bodies 
have  extension."  Such  judgments  are,  by  no  means,  void  of 
consequence,  inasmuch  as  they  render  clear  and  distinct  our 
conceptions  of  their  objects. 

An  implied  judgment  is  one  which  is  really  only  another  form 
of  another  judgment,  but  which  presents  some  important  ele- 
ment of  the  latter  which  was  not  distinctly  expressed  before. 
We  often  say :  If  this  proposition  is  true,  that  is  also  true,  be- 
cause the  latter  is  really  implied  in  the  former,  that  is,  is  only  a 
different  form  of  stating  the  same  thing.     Implied  judgments 


JUDGMENTS.  65 

have  a  very  important  use  ;   indeed,  a  statement  of  them  is 
often  indispensable  to  the  production  of  conviction. 

Axioms,  Postulates,  Problems,  and  Theorems. 

An  axiom  is  an  analytical  judgment  (analytical  or  intuitive 
synthetical  judgment  of  Kant)  which  may  be  employed  as  a 
principle  in  the  sciences  in  general,  that  is,  a  judgment  by 
which  other  judgments  may  be  evinced.  As  shown  in  the  In- 
tellectual Philosophy,  pp.  257-8,  the  axioms  which  constitute 
the  foundation-principles  of  each  of  the  sciences  are  essentially 
identical  with  those  of  every  other. 

Postulates  are  analytical  judgments  which  can  be  employed 
as  principles  only  in  particular  sciences.  Thus  the  axiom, 
"  Things  equal  to  the  same  things  are  equal  to  one  another,"  is 
really,  though  often  stated  in  a  somewhat  different  form,  iden- 
tical with  that  which  lies  at  the  basis  of  every  science  that  can 
be  named  ;  while  the  postulate,  "  That  a  straight  line  may  be 
drawn  between  any  two  points  in  space,"  pertains  exclusively 
to  geometry  and  kindred  sciences. 

A  problem  is  a  judgment  which  appears  neither  true  nor 
false,  and  requires  an  answer  to  the  question,  Is  it,  or  is  it  not 
true  ?  or  presents  a  number  of  judgments  either  of  which  appa- 
rently may  be  true,  and  but  one  can  be,  and  requires  an  answer 
to  the  question,  Which  is  true  ?  or  finally  affirms  that  a  certain 
thing  may  be  done,  and  requires  an  answer  to  the  question, 
How  may  it  be  done?  In  problems  of  the  first  and  second 
classes  above  named,  an  annwer  of  this  kind  is  most  commonly 
required,  to  wit,  not  what  is,  or  what  is  not  true,  in  the  particular 
cases  presented,  but  how  may  we  determine,  what  is,  and  what 
is  not  true,  in  these  cases  ?  In  the  solution  of  particular  prob- 
lems, in  this  form,  wre  obtain  not  only  answers  to  the  specific 
questions  presented,  but  principles  by  which  all  other  similar 
questions  may  be  solved.  Let  us  suppose,  for  example,  that  an 
event  like  the  raising  of  Lazarus  from  the  dead  occurs  in  our 
presence.  The  question  presents  itself,  Is  this,  or  is  it  not  a 
real  miracle  ?  or,  Is  this  event  the  result  of  the  direct  and  im- 


66  LOGIC. 

mediate  interposition  of  creative  power,  or  of  mere  natural 
causes  ?  In  the  first  form,  we  have  a  problem  of  the  first  class 
named,  and  in  the  other  of  the  second.  Suppose,  that  we  are 
required  not  merely  to  give  a  direct  answer  to  these  questions, 
but  to  give  criteria  by  which  we  may  know  whether  the  event 
is,  or  is  not,  a  miracle,  or  whether  it  was  the  result  of  a  super- 
natural interposition  of  creative  power,  or  of  natural  causes. 
In  giving  the  solution  in  this  form,  we  should  not  only  obtain 
an  answer  to  the  specific  questions  above  stated,  but  should  also 
obtain  criteria  by  which  we  can,  in  all  other  cases,  distinguish 
events  resulting  from  natural  causes  from  real  miracles.  Sup- 
pose, on  the  other  hand,  we  are  required  to  give  a  rule,  by 
which  a  given  line  may  be  divided  into  any  specific  number  of 
equal  parts.     We  then  have  a  problem  of  the  third  class. 

Theorems  are  theoretical  judgments  capable  of  proof,  and  re- 
quiring it ;  as,  for  example,  the  proposition,  "  All  the  angles  of  a 
triangle  are  equal  to  two  right  angles." 

Corollaries,  Lemmas,  and  Scholia. 

Corollaries  are  the  immediate  and  intuitive  consequences  of 
preceding  judgments. 

A  lemma  is  a  judgment  previously  evinced,  and  now  used  as 
a  principle  in  the  demonstration  of  other  judgments.  In  gen- 
eral it  is  not  native  in  the  paiticular  science  in  which  it  is  presup- 
posed as  evinced,  but  is  taken  from  some  other  science,  as  when 
some  ascertained  truth  in  the  science  of  geology,  for  example, 
is  employed  as  a  principle  in  the  science  of  natural  theology. 

Scholia  are  explanatory  notes  or  observations  appended  to 
evinced  judgments,  for  the  purpose  of  illustration. 

CEITEEIA    OF    JUDGMENTS,    OE   CHABACTEEISTICS    OF   ALL   VALID 
JUDGMElSrrS. 

We  are  now  prepared  to  give  the  universal  criteria  of  judg- 
ments, or  the  universal  and  necessary  characteristics  of  all  valid 
judgments,  as  distinguished  from  those  which  are  not  valid. 


1 


JUDGMENTS.  67 


General  Criteria. 


All  universally  valid  judgments  must  have  the  following  char- 
acteristics : 

1.  The  conceptions  constituting  the  subject  and  predicate  of 
such  judgments  must  be  valid  according  to  the  criteria  devel- 
oped in  the  last  chapter. 

2.  The  judgment  must  be  analytical  according  to  the  defini- 
tion above  given  of  such  judgments. 

Or,  3.  It  must  be  evinced  as  true,  by  means  of  judgments 
which  are  analytical. 

All  valid  primitive  judgments  have  the  first  two  characteris- 
tics. All  valid  derivative  ones  have  all  the  three  together. 
Any  judgment  wanting  these  characteristics  must  be  held  as 
not  valid. 

Particular  and  special  Criteria. 

As  necessarily  involved  in  the  above  criteria,  we  present  the 
following  particular  and  special  ones. 

Judgments  relative  to  all  valid  Conceptions. 

1.  All  judgments  must  be  held  as  valid  in  which  any  ele- 
ment of  any  valid  conception  is  affirmed  of  the  object  or  ob- 
jects of  such  conception.  Suppose,  for  example,  that  the  con- 
ception represented  by  the  term  man,  be  assumed  as  valid, 
then  any  judgment  in  which  any  or  every  element  of  that  con- 
ception is  affirmed  of  all  men  or  any  one  individual  of  the  race, 
must  be  held  as  valid.  So  of  all  similar  judgments  relative  to 
all  valid  conceptions. 

2.  All  judgments  must  be  held  as  valid,  in  which  the  neces- 
sary relations  between  a  valid  conception  and  its  logical  ante- 
cedent, or  between  any  element  of  such  conception  and  the  log- 
ical antecedent  of  that  element,  are  affirmed ;  as,  for  example, 
the  judgments,  ".Body  supposes  space ;  succession  time ;  events 
a  cause ;  and  phenomena  substance,"  &c. 


3.  All  judgments  must  be  held  as  valid  which  affirm  the  im- 
mediate and  necessary  consequence  of  valid  judgments.  In 
other  words,  when  one  judgment  must  be  held  as  valid,  all 
Others  immediately  implied  in  it  must  be  held  as  valid  also.  If 
the  judgment,  "  Every  event  must  have  a  cause,"  is  valid,  then 
the  judgment,  "  Every  event  must  have  a  cause  adequate  and 
adapted  to  produce  that  event,"  must  be  held  as  valid  also. 
If  the  judgment,  "  Phenomenon  or  quality  supposes  substance," 
is  valid,  the  judgment,  "  Substances  are  as  their  phenome- 
na or  qualities,"  must  be  held  as  valid  also.  So  in  all  other 
instances. 

INDIVIDUAL  (SINGLE),  PARTICULAR,  AND  UNIVERSAL  JUDGMENTS. 

Individual  Judgments  affirmative. 

In  regard  to  every  individual  (each  particular  object),  the 
following  judgments  must  be  held  as  true  : 

1.  AH  judgments  which  affirm  of  such  object  any  element  of 
any  valid  conception  pertaining  to  it.  Such  judgments,  being 
really  analytical,  must  be  valid. 

2.  All  judgments  which  affirm  of  said  object  that  it  belongs 
to  any  class  of  objects  with  which  it  has  common  characteris- 
tics, the  characteristics  which  peculiarize  that  class. 

3.  All  judgments  which  affirm  of  such  object  any  or  all  of 
the  elements  of  the  conception  which  represent  that  class. 

4.  All  judgments  which  affirm  of  that  individual  any  or  all  of 
the  elements  embraced  in  any  superior  conception  of  that  just 
named. 

The  judgment,  in  the  first  instance,  is  really,  as  said  above, 
analytical,  and  cannot  but  be  valid.  In  the  second  case,  we 
have  the  universal  and  immutable  law  of  classification.  Each 
object  must  take  rank  with  all  others  with  which  it  has  common 
characteristics.  The  third  case  is  necessarily  involved  in  the 
second  ;  for  these  are  the  necessary  conditions  of  an  object  be- 
ing entitled  to  take  rank  with  a  certain  class.  When,  there- 
fore, it  is  known  to  belong  to  a  certain  class  it  is,  and  must  be, 


JUDGMENTS.  69 

recognized  as  possessed  of  all  the  elements  embraced  in  the  con- 
ception which  represents  that  class,  and  all  judgments  which 
affirm  of  it  any  or  all  of  such  elements  must  he  valid.  The  ele- 
ments embraced  in  the  superior  conceptions  are  embraced  in  the 
inferior.  When  all  of  the  former  may  be  affirmed  of  an  object, 
of  course  any  or  all  of  the  latter  may  be.  All  judgments  of  the 
fourth  class,  therefore,  must  be  valid. 

Individual  Judgments  {negative). 

The  following  negative  judgments  in  regard  to  such  objects 
must  be  held  as  valid  : 

1.  All  judgments  which  deny  of  said  object  any  and  all  ele- 
ments and  characteristics  incompatible  with  any  and  all  ele- 
ments of  valid  conceptions  and  judgments  in  regard  to  it. 
When  a  given  characteristic  may  be  affirmed  of  any  object, 
every  thing  incompatible  with  that  characteristic  may  of 
course  be  denied  of  it.  When,  for  example,  it  is  admitted  that 
matter  has  the  quality  of  extension,  and  it  is  affirmed  that  the 
substance  itself,  in  regard  to  its  ultimate  essence,  is  unknown  to 
us,  it  may  be  denied  absolutely  that  there  is,  or  can  be,  in  such 
substance,  any  thing  incompatible  with  the  idea  of  extension, 
and  the  judgment,  that  any  theory  in  regard  to  the  nature  of 
that,  substance  (any  ontological  conception  of  it)  that  affirms 
that  it  is  not  in  reality  an  extended  substance,  is  and  must  be 
false,  must  be  held  as  valid.     So  in  all  other  cases  of  the  kind. 

2.  When  it  is  undeniably  true,  that  if  an  object  does  or  did 
possess  certain  characteristics,  those  characteristics  would  ap- 
pear, that  is,  would  be  given  in  intuition,  and  they  do  not  ap- 
pear, and  have  not  appeared  (are  not  given  in  intuition),  then 
the  judgments,  which  deny  such  characteristics  of  such  objects, 
must  be  held  as  valid.  It  is  undeniable,  for  example,  that  if 
Washington  was  under  the  controlling  ambition  of  possessing 
monarchical  or  despotic  power,  he  would,  in  the  circumstances 
in  which  he  was  placed,  have  attempted  to  have  gained  that 
power  over  his  countrymen,  and  the  fact  of  such  attempt  would 
appear.     The  absence  of  the  fact,  renders  valid  the  judgment, 


70  LOGIC. 

that  he  was  not  under  the  control  of  the  principle  before  us. 
Again  :  if  spontaneous  production  and  the  transmutation  of  spe- 
cies are  the  law  of  nature,  and  the  order  of  creation,  we  should 
find  somewhere  in  the  present  or  past  history  of  the  earth,  un- 
deniable facts  indicative  of  the  truth  of  such  theory.  The  total 
absence  of  any  such  facts  within  the  knowledge  of  man,  since 
his  existence  on  earth,  and  the  total  absence  of  all  abnormal 
specimens,  of  any  intermediate  creations,  in  the  vast  laboratory 
of  geological  science,  render  undeniably  valid  the  judgment, 
"  That  the  theory  of  spontaneous  production  and  transmutation 
of  species  is  not,  and  cannot  be  true."  Very  few  of  the  laws  of 
thought  are  of  more  importance  than  that  under  consideration, 
when  legitimately  employed. 

3.  All  negative  judgments  are  valid,  which  in  matter,  though 
not  in  form,  are  identical  with  valid  affirmative  ones.  If  the 
judgment,  "A  is  mortal,"  is  valid,  the  judgment,  "A  is  not 
immortal,"  is  also  valid,  inasmuch  as  the  two  propositions  mere- 
ly affirm  one  and  the  same  thing.  In  argument,  it  is  often  ex- 
pedient to  state  an  affirmative  judgment  in  its  equivalent  nega- 
tive form. 

A  careful  examination  will  show,  we  judge,  that  all  valid  indi- 
vidual judgments  fall  under  one  or  the  other  of  the  classes 
above  named,  and  that  no  judgment  not  belonging  to  one  or 
the  other  of  these  classes  should  be  held  as  valid. 

Particular  (pluratave)  Judgments. 

All  particular  judgments  of  the  following  classes  must  be  held 
as  valid : 

1.  All  judgments  of  this  class  which  rank  as  subaltern  judg- 
ments under  universal  ones  which  are  valid.  What  is  true  of 
every  member  of  a  given  class,  may  of  course  be  affirmed  to  be 
true  of  some  members  of  that  class. 

2.  When  a  certain  characteristic,  or  quality,  belongs  to  ajpart, 
but  not  to  all,  of  the  members  of  a  certain  class,  particular  judg- 
ments which  affirm  that  some  of  the  members  of  that  class  have 
guch  characteristic  or  quality,  must  be  held  as  valid. 


JUDGMENTS.  71 


3.  In  all  such  cases,  the  particular  negative  judgment  which 
denies  that  characteristic  or  quality  of  some  member  of  the  class 
under  examination,  must  he  valid  also.  As  wisdom,  for  exam- 
ple, pertains  to  a  part,  and  not  the  whole,  of  the  human  race, 
the  particular  judgments,  "Some  men  are  wise,  and  some  men 
are  not  wise,"  must  be  held  as  valid.     So  in  all  similar  instances. 

Universal  Judgments  {affirmative). 

All  affirmative  universal  judgments  are  valid  which  have 
either  of  the  following  characteristics,  or  all  of  them  together : 

1.  Those  in  which  any  or  all  of  the  elements  embraced  in 
the  conception  which  represents  a  class  of  objects,  are  affirmed 
of  all  the  members  of  that  class — any  judgment,  for  example, 
which  affirms  of  all  men  any  or  all  of  the.  elements  of  the  con- 
ception represented  by  the  term  man. 

2.  All  which  affirm  universally  of  such  a  class  any  or  all  of 
the  elements  embraced  in  any  conception,  to  which  the  concep- 
tion representing  that  class  sustains  the  relation  of  an  inferior 
conception,  that  is,  we  may  affirm  of  all  the  objects  of  a  specifi- 
cal  conception,  any  or  all  of  the  elements  of  any  of  its  superior 
or  generical  conceptions. 

3.  All  judgments  which  affirm  of  all  the  members  of  a  class 
any  or  all  the  elements  embraced  in  the  characteristic  concep- 
tion of  such  class. 


's  (negative). 

All  negative  universal  judgments  must  be  admitted  as  valid 
which  have  the  following  characteristics : 

1.  All  which  deny  of  all  the  members  of  any  one  class  or 
species  any  or  all  of  the  elements  of  any  opposite  specifical  con- 
ception, those  elements  excepted  which  belong  to  superior  con- 
ceptions under  which  each  of  the  above  take  rank  as  inferior 
ones. 

Thus,  if  we  should  deny  of  the  conception  represented  by  the 
term  apple,  any  or  all  of  the  elements  of  the  conception  repre- 


72  LOGIC. 

sented  by  the  terra  peach,  with  the  exception  of  those  embraced 
in  the  superior  conception  represented  by  the  term  fruit,  the 
affirmation  would  be  valid,  and  that  for  the  reason,  that  species 
under  a  genus  are  formed  exclusively  on  the  principle  of  contra- 
diction.   The  same  will  hold  equally  true  in  all  other  similar  cases; 

2.  All  judgments  in  which  any  and  all  characteristics  incom- 
patible with  any  or  all  the  elements  of  any  valid  conception,  are 
denied  of  all  objects  represented  by  such  conceptions.  We  may 
affirm  absolutely,  for  example,  that  no  untruth  was  ever  given 
forth  by  inspiration  of  the  Almighty.  The  reason  is  obvious.  The 
thing  denied  is  incompatible  with  all  valid  conceptions  of  Deity. 

3.  All  universal  negative  judgments  must  be  held  as  valid 
which  are  really  equivalent  to  valid  affirmative  ones.  Thus  the 
judgment,  "  No  man,  physically  considered,  is  immortal,"  must 
be  held  as  valid,  because  it  is  in  fact  equivalent  to  the  universal- 
ly valid  judgment  expressed  by  the  proposition,  "  All  men  are 
mortal."  It  is  often  of  great  importance,  thus  to  substitute  for 
a  valid  affirmative  judgment,  its  equivalent  negative  one. 

4.  When  it  is  undeniable,  that  a  given  characteristic,  if  it  did 
attach  to  any  member  of  a  given  class,  would  be  given  by  intui- 
tion in  connection  with  some  members  of  the  same,  and  is  not 
given,  then  the  judgment  which  denies  such  characteristic  of 
all  the  members  of  that  class,  must  be  held  as  valid.  Thus  the 
judgment,  "  No  plant  is  produced  but  through  a  seed,  and  no 
seed  but  through  a  plant,"  must  be  held  as  valid,  because  it  is 
undeniable,  that  if  the  opposite  judgments  were  true,  facts  cor- 
roborative of  them  would  appeal*. 

It  is  believed,  that  all  valid  universal  negative  judgments  be- 
long to  one  or  the  other  of  the  classes  above  defined,  and  that 
we  have  here  fundamental  criteria  by  which  to  determine  the 
validity  of  such  judgments. 

Judgments  pertaining  to  the  objects  of  inferior  and  superior 
conceptions. 

All  that  is  required  to  be  said  relating  to  judgments  pertain- 
ing to  the  objects  of  inferior  and  superior  conceptions,  has  al- 


JUDGMENTS.  73 

ready  been  anticipated,  and  what  is  added,  in  this  connection, 
is  only  for  the  sake  of  distinctness.  On  this  subject  we  would 
simply  add,  that  all  judgments  relative  to  such  objects  must  be 
held  as  valid  which  have  the  following  characteristics  : 

1.  All  judgments  in  which  any  object  or  class  of  objects  hav- 
ing the  elements  represented  in  any  conception  is  ranked  or 
classed  under  that  conception. 

2.  All  judgments  which  affirm  of  any  object  of  an  inferior 
conception,  not  only  any  or  all  of  the  elements  of  that  particular 
conception,  but  any  or  all  of  those  of  any  superior  one. 

Judgments  pertaining  to  the  objects  of  characteristic  concep- 
tions (affi 


When,  an  object  agrees  with  a  characteristic  conception,  or 
possesses  the  elements  embraced  in  such  conception,  the  follow- 
ing judgments  relative  to  it  must  be  held  as  valid : 

1.  Any  which  rank  said  object  with  the  class  to  which  the 
conception  under  consideration  pertains. 

2.  All  judgments  which  affirm  of  said  object  any  or  all  the 
elements  of  the  conception  which  represents  that  class,  or  all  or 
any  of  the  elements  of  any  superior  conception. 

Suppose,  for  example,  that  an  object  is  before  us,  that  agrees 
with  the  characteristic  conception  of  the  class  of  substances  rep- 
resented by  the  term  gold.  For  no  other  reason,  we  may  af- 
firm, that  the  object  is  gold,  that  it  has  any  or  all  of  the  proper- 
ties of  gold.  We  may  affirm,  further,  that  it  is  a  metal,  a  min- 
eral ;  that  it  is  matter,  a  substance  ;  or  affirm  of  it  any  or  all  of 
the  elements,  of  any  or  of  all  the  conceptions  which  these  terms 
represent.     So  in  all  other  instances. 

Judgments  relative  to   objects    of  characteristic    conceptions 
{negative). 

Of  all  objects  agreeing  with  characteristic  conceptions,  the 
following  negative  judgments  must  be  held  as  valid  : 

1.  All  which  deny  of  such  objects  any  or  all  the  elements 
represented  in  any  opposite  specifical  conception,  those  excepted 


74  LOGIC. 

which  are  represented  in  the  common  superior  conceptions. 
Thus,  for  example,  if  an  object  has  the  characteristic  elements 
of  gold,  we  may  affirm,  from  such  fact,  that  such  object  is  not 
silver,  copper,  platinum,  &c,  and  deny  of  it  any  of  the  peculiar 
and  specifical  qualities  of  such  metals.     So  in  all  other  instances. 

2.  All  judgments  which  deny  of  such  objects  any  or  all  of  the 
elements  represented  by  any  incompatible  conception.  Thus, 
if  we  should  affirm  that  any  act  having  the  undeniable  charac- 
teristics of  an  act  of  perjury,  did  not  proceed  from  an  honest 
intention  to  speak  the  truth,  the  judgment  would  be  valid. 

3.  All  negative  judgments  which  are  equivalent  to  valid  af- 
firmative ones.  In  other  connections,  this  principle  has  received 
a  sufficient  elucidation.  Nothing,  therefore,  need  be  added  in 
respect  to  it  here. 

HYPOTHETICAL   JUDGMENTS. 

It  is  a  somewhat  remarkable  fact,  that  while  all  systems  of 
logic  treat  of  hypothetical  and  disjunctive  judgments,  in  no 
such  treatises  do  we  find,  so  far  as  our  knowledge  extends,  even 
an  attempt  to  give  us  any  criteria  by  which  we  may  determine 
the  validity  of  either  class  of  these  judgments.  We  will,  there- 
fore, attempt  the  accomplishment  of  this  important  result. 

Hypothetical  Judgments  classed. 

All  hypothetical  judgments  may  be  divided  into  three  classes  : 
1.  Those  in  which  the  antecedent  and  consequent  have  different 
predicates,  and  each  the  same  subject ;  as,  "  If  A  is  in  B,  it  is,  or 
is  not,  in  C."  2.  Those  in  which  both  have  the  same  predicate, 
and  each  a  different  subject :  "  If  A  is  in  B,  C  is,  or  is  not,  in  B." 
3.  Those  in  which  both  have  different  subjects,  and  different 
predicates :  "If  A  is  B,  C  is,  or  is  not,  D." 

Criteria  of  such  Judgments. 

Judgments  of  the  first  class  are  valid,  when,  and  only  when, 
the  predicate  of  the  consequent  may  be  affirmed  or  denied  uni- 


JUDGMENTS.  15 


ersally,  as  the  case  may  be,  of  the  predicate  of  the  antecedent. 
Thus,  the  judgment,  "If  A  is  in  B,  it  also  is' in  C,"  can  be  valid 
only  when  the  judgment,  "  Every  B  is  in  C,"  is  valid ;  and  the 
former  judgment  must  be  valid  when  the  latter  is.  So,  also,  we 
can  affirm  that,  "  If  A  is  in  B,  it  is  not  in  C,"  when,  and  only 
when,  the  judgment,  "B  is  never  in  C,"  is  valid;  and  in  that 
case,  the  former  judgment  must  be  true. 

Judgments  of  the  second  class'  are  valid,  when,  and  only 
when,  the  subject  of  the  antecedent  may  be  affirmed  or  denied, 
as  the  case  may  be,  universally  of  the  subject  of  the  consequent. 
Thus,  the  judgment,  "If  A  is  in  B,  C  is  in  B,"  can  be  true  but 
upon  the  supposition  that  C  is  always  in  A,  and  must  be  true  in 
that  case.  The  judgment,  in  its  negative  form,  can  be  true, 
but  upon  the  supposition,  that  C  is  never  in  A,  and  must,  in 
that  case-,  be  always  true. 

Judgments  of  the  third  class  can  be  true,  but  upon  the  con- 
dition that  the  relations  between  the  subject  and  predicate  of 
the  antecedent,  are  the  same  as  between  the  subject  and  predi- 
cate of  the  consequent.  Equality  or  similarity  of  relations  is 
the  thing,  and  the  only  thing,  really  affirmed  or  denied  in  all 
such  judgments.  Unless,  therefore,  the  judgment,  "A  sustains 
similar  relations  to  B  that  C  does  to  D,"  is  valid,  the  judgment, 
"  If  A  is  B,  C  is  D,"  cannot  be  valid.  On  the  other  hand,  when 
the  former  judgment  is  valid,  the  latter,  of  course,  must  be. 
These  remarks  are  so  manifestly  applicable  to  these  judgments 
when  given  in  the  negative  form,  that  nothing  is  called  for  on 
this  point. 

"What  may  be  affirmed,  when  the  relations  referred  to  are 
equal,  may  be  affirmed  when  the  relations  are  greater  in  de- 
gree. If,  for  example,  we  may  say  that  A,  possessing  $100,  is 
able  to  meet  an  indebtedness  amounting  to  that  sum,  we  may 
of  course  affirm,  that  B,  possessing  $10,000,  is  able  to  discharge 
an  indebtedness  amounting  to  $1,000. 


76 


^Disjunctive  Judgments. 


Disjunctive  judgments  always  partake  of  one  or  the  other  of 
these  characteristics.  A  fact,  or  a  class  of  facts  (A),  is  known 
to  exist,  and  their  explanation  is  required.  A  certain  given 
number  of  hypotheses,  B,  C,  D,  &c,  two  or  more,  present  them- 
selves, none  others  being,  from  the  nature  of  the  case,  conceiva- 
ble or  possible,  while  one  of  them,  to  the  exclusion  of  all  the 
others,  must  be  true.  Hence  we  say,  "  A  must  be  in  B,  C,  or  D." 
A  judgment  of  this  class  is  valid,  when  the  facts  A,  are  known 
to  exist,  and  when  all  conceivable  demonstrable  judgments  are 
specified  in  the  judgment,  "A  is  in  B,  C,  or  D,"  &c,  and  when, 
from  the  character  of  the  facts,  A  must  be  found  in  one  of  these 
judgments,  B,  C,  or  D,  to  the  exclusion  of  each  of  the  others. 
Each  judgment  must  be,  in  its  nature,  exclusive,  and  the  whole 
together  must,  undeniably,  exhaust  the  subject :  for,  if  any  one 
conceivable  hypothesis  is  not  included,  the  judgment  is  not 
valid. 

Or  it  may  be  known  that  there  is  a  cause,  X,  for  a  given  class 
of  facts,  and  the  inquiry  is,  what  is  the  nature  of  this  cause  ? 
From  the  nature  of  the  case,  there  can  be  but  a  certain  num- 
ber of  answers  to  this  question,  and  one  of  these,  to  the  exclu- 
sion of  each  and  all  the  others,  must  be  true.  In  such  a  case, 
we  say,  "  X  is  A,  B,  or  C."  Such  a  judgment  is  valid,  when  it 
undeniably  embraces  all  conceivable  or  possible  answers,  and 
when  each  member  of  the  judgment  is  in  such  disjunction  with, 
or  opposition  to  each  and  all  of  the  others,  that  one  of  them,  to 
the  exclusion  of  each  and  all  the  others,  must  be  true.  If  any 
possible  answer  to  the  question  is  omitted,  or  if  each  proposi- 
tion is  not,  in  its  nature,  exclusive  of  each  and  all  the  others, 
then  the  judgment  is  not  valid.  For  example,  All  men  be- 
lieve, and  must  believe,  that  there  is  an  ultimate  reason  why 
the  facts  of  the  universe  are  what  they  are,  and  not  otherwise. 
Let  X,  for  example,  represent  this  ultimate  or  unconditioned 
cause.  Now  it  is  self-evident,  that  this  cause  X,  must  be  an  in- 
herent law,  or  principle  of  nature,  which  we  will  call  L,  or  a 
power  out  of  and  above  nature,  which  we  will  denominate  G, 


the 


PROPOSITIONS.  11 


ie  god  of  theism.  Hence,  the  judgment,  "  X  is  L  or  G,"  must 
be  valid. 

There  is  one  form  of  the  disjunctive  judgment  which,  oJ 
course,  must  be  valid,  to  wit :  "  Every  X  is  A,  or  not  A  ;"  a 
form  of  judgment  which  hardly  differs  from  the  tautological, 
and  requires  no  elucidation. 

We  believe  that  all  disjunctive  judgments  belong  to  one  01 
the  other  of  the  above  classes,  and  that  we  have,  in  the  princi 
pies  above  given,  universal  criteria  of  their  validity. 


Section  II. — Of  Propositions. 

Having  treated  sufficiently  of  judgments,  it  remains  to  make 
a  few  remarks  in  respect  to  propositions,. which  are  judgments 
expressed  in  words.  Logic  treats  only  of  assertative  proposi- 
tions, those  which  affirm  or  deny  ;  as,  "  A  is  B,  or  A  is  not  B." 

Quality  and  Quantity  of  Propositions,  &c. 

Propositions,  when  contemplated  with  reference  to  their  na- 
ture or  substance,  are  divided  into  two  classes,  to  wit :  categori- 
cal, those  which  simply  affirm  or  deny,  as,  "  A  is,  or  is  not,  B  ;" 
and  hypothetical,  those  which  affirm  conditionally,  as,  "  If  A  is 
B,  C  is  D,»  &c. 

When  contemplated  with  reference  to  their  quality,  they  are 
divided  as  affirmative  :  " A  is  B  ;"  or  negative,  "A  is  not  B." 

In  regard  to  the  quantity,  they  are  divided  into  universal, 
those  in  which  the  predicate  is  affirmed  or  denied  of  all  the  ob- 
jects represented  by  the  subject ;  as,  "  Every  A  is  B,  or  no  A 
is  B  ;"  and  particular,  those  in  which  the  predicate  is  affirmed 
or  denied  of  a  part  only  of  the  objects  represented  by  the  sub- 
ject. As  affirmative  and  negative  propositions  are  each  divided 
into  two  classes,  universal  and  particular,  we  have  four  kinds  of 
propositions :  the  universal  affirmative,  which  is  represented  by 
the  term,  A ;  the  universal  negative,  E  ;  the  particular  affirma- 
tive, I ;  and  the  particular  negative,  O. 


IS 


Distribution  of  Terms. 

When  a  term  stands  for  all  its  significates,  that  is,  for  every 
individual  of  the  class  which  it  represents,  then  it  is  said  to  be 
distributed.  When  it  represents  apart  only  of  its  significates, 
then  it  is  said  to  be  not  distributed. 

When  the  subject  of  a  proposition  is  a  common  term,  its  dis- 
tribution is  commonly  signified  by  such  terms  as  "  All,  every, 
no,"  &c. ;  and  when  not  distributed,  by  the  term  "  Some,"  &c. 
When  no  sign  is  used,  the  question,  whether  the  subject  is  to  be 
understood  as  distributed  or  not,  is  always  to  be  determined 
by  the  particular  circumstances  of  the  case,  and  not  by  a  refer- 
ence to  the  matter  of  the  proposition.  The  quantity  of  a  propo- 
sition, when  no  signs  are  used  to  indicate  the  distribution  or 
non-distribution  of  terms,  "  is  ascertained,"  says  Dr.  Whately, 
"  by  the  matter,  i.  e.  the  nature  of  the  connection  between  the 
extremes,  which  is  either  necessary,  impossible,  or  contingent. 
In  necessary  and  impossible  matter,  an  indefinite  is  understood 
as  a  universal ;  e.  g.  *  Birds  have  wings,'  i.  e.  all  birds  ;  '  Birds 
are  not  quadrupeds,'  i.  e.  none.  In  contingent  matter  (i.  e. 
where  the  terms  partly — i.  e.  sometimes — agree,  and  partly 
not),  an  indefinite  is  understood  as  a  particular;  e.  g.  'Food 
is  necessary  to  life,'  i.  e.  some  food ;  '  Birds  sing,'  i.  e.  some 
do ;  '  Birds  are  not  carnivorous,'  i.  e.  some  are  not,  or,  all 
are  not." 

Here  are  two  fundamental  mistakes  relatively  to  the  science 
of  logic, — the  supposition  that  this  science  has  any  thing  to  do 
with  the  matter  of  the  proposition — and  the  supposition  that  in- 
dividuals always  conform,  in  their  use  of  terms,  to  the  rules 
which  our  author  has  laid  down ;  whereas  the  opposite  is  not 
unfrequently  the  case,  and  we  should  violate  all  the  laws  of  lan- 
guage should  we  interpret  their  words  according  to  any  such 
rules. 

Apply  the  principle  we  have  laid  down  to  the  cases  cited  by 
Dr.  Whately,  and  we  shall  at  once  see  its  validity.  Suppose 
that  the  question  is  being  argued,  whether,  as  a  matter  of  fact, 


aU 


PROPOSITIONS.  79 


birds  have  wings.  The  individual  maintaining  the  affirma- 
tive uses  the  phrase,  "  Birds  have  wings ;"  and  on  the  opposite 
side  it  is  affirmed,  "  Birds  have  not  wings."  The  circum- 
stances of  the  case  require  us  to  understand  the  first  proposition 
as  universal,  and  the  second  as  particular,  that  is,  the  contra- 
dictory of  the  first.  If,  on  the  other  hand,  the  question  was 
this,  "  Are  any  birds  quadrupeds  ?"  and,  on  one  side,  it  should 
be  affirmed,  "  Birds  are  quadrupeds,"  and  on  the  other,  "  Birds 
are  not  quadrupeds,"  we  should  be  bound,  by  the  circumstances 
of  the  case,  to  assume  the  first  proposition  as  particular,  and 
the  second  as  universal.     So  in  all  other  circumstances. 

Singular  propositions,  those  in  which  the  subject  is  a  proper 
name,  or  a  common  term,  with  a  singular  sign,  are  reckoned  in 
logic  as  universals,  because  in  such  cases  the  predicate  is  af- 
firmed of  the  whole  subject.  The  following  quotation  from 
Dr.  Whately  presents  the  rules  of  distribution  pertaining  to 
the  subject  and  predicate  of  propositions  as  commonly  given, 
so  distinctly,  that  we  give  it,  without  note  or  comment  of 
our  own : 

"  It  is  evident,  that  the  subject  is  distributed  in  every  univer- 
sal proposition,  and  never  in  a  particular  (that  being  the  very 
difference  between  universal  and  particular  propositions)  ;  but 
the  distribution  or  non-distribution  of  the  predicate  depends 
(not  on  the  quantity,  but)  on  the  quality  of  the  propositions ; 
for,  if  any  part  of  the  predicate  agrees  with  the  subject,  it  must 
be  affirmed,  and  not  denied  of  the  subject ;  therefore,  for  an 
affirmative  proposition  to  be  true,  it  is  sufficient  that  some  part 
of  the  predicate  agrees  with  the  subject ;  and  (for  the  same 
reason)  for  a  negative  to  be  true,  it  is  necessary  that  the  whole 
of  the  predicate  should  disagree  with  the  subject ;  e.  g.  it  is 
true  that  '  Learning  is  useful,'  though  the  whole  of  the  term 
'  useful'  does  not  agree  with  the  term  '  learning,'  (for  many 
things  are  useful  besides  learning)  ;  but,  '  No  vice  is  useful,' 
would  be  false,  if  any  part  of  the  term  '  useful'  agreed  with  the 
term  '  vice'  (i.  e.  if  you  could  find  any  one  useful  thing  which 
was  a  vice).  The  two  practical  rules,  then,  to  be  observed  re- 
specting distribution,  are : 


"  1st.  All  universal  propositions  (and  no  particular)  distribute 
the  subject. 

"  2d.  All  negative  (and  no  affirmative)*  the  predicate.  It 
may  happen,  indeed,  that  the  whole  of  the  predicate,  in  an 
affirmative,  may  agree  with  the  subject ;  e.  g.  it  is  equally  true, 
that  '  All  men  are  rational  animals ;'  and,  '  All  rational  ani- 
mals are  men ;'  but  this  is  merely  accidental,  and  is  not  at  all 
implied  in  the  form  of  expression,  which  alone  is  regarded  in 
logic." 

Of  Opposition. 

Propositions  are  said  to  be  opposed  to  each  other,  when  the 
subject  and  predicate  are  the  same,  and  they  differ  in  quantity, 
quality,  or  both. 

In  respect  to  quantity,  A  and  E  are  each  opposed  to  I  and  O. 
From  the  nature  of  this  opposition,  the  following  rules,  pertain- 
ing to  the  validity  of  propositions,  arise : 

1.  If  the  universal  is  valid,  so  is  the  particular;  that  is,  if  A  is 
true,  I  must  be  true  also  ;  and  if  E  is  true,  O  must  be.  If  the 
proposition,  "  All  men  are  mortal,"  is  true,  I,  which  affirms  that 
"  Some  men  are  mortal,"  must  be  true  also.  If  the  proposition, 
"No  birds  are  quadrupeds,"  is  true,  O,  which  affirms  that 
"  Some  birds  are  not  quadrupeds,"  must  also  be  true. 

2.  If  the  particular,  I  or  O,  be  false,  its  respective  universal, 
A  or  E,  must  be  false  also ;  in  other  words,  the  denial  of  the 
particular  involves  a  denial  of  the  universal  under  which  the 
former  ranks.  If  the  proposition,  "  Some  men  are  mortal,"  is 
false,  A,  which  affirms  that  "  All  men  are  mortal,"  cannot,  of 
course,  be  true.  So  if  the  proposition,  "  Some  men  are  not  im- 
mortal," is  false,  E,  which  affirms  that  "  No  man  is  immortal," 
must  be  false  also. 

3.  On  the  other  hand,  both  the  universals  (A  and  E)  may  be 
false,  and  both  the  particulars  (I  and  O)  may  be  true ;  that  is, 
the  denial  of  the  universal  does  not  necessitate  a  denial  of  the 
particular.     The  propositions,  "  All  men  are  liars,"  and  "  No 

*  Here,  as  we  shall  see  hereafter,  is  a  fundamental  mistake  in  the  science  of  logia 


PROPOSITIONS.  81 

men  are  liars,"  may  both  be  false  ;  and  the  propositions,  "  Some 
men  are  liars,"  and  "  Some  men  are  not  liars,"  may  be  true. 

In  respect  to  quality,  A  and  I  are  each,  respectively,  opposed 
to  E  and  O,  and  vice  versa.  The  two  universale  are  opposed 
throughout  their  whole  extent ;  that  is,  what  one  affirms  in  re- 
gard to  a  whole  class,  the  other  denies  in  regard  to  every  indi- 
vidual of  that  class.  The  universal  of  one  is  opposed  to  the  par- 
ticular of  the  opposite  quality,  A  to  O,  E  to  I,  simply  and  ex- 
clusively, in  regard  to  one  point,  the  question  of  universality. 
What  the  universal  affirms  as  true  of  every  individual  of  a 
certain  class,  the  opposite  particular  denies  in  regard  to  some 
individuals  of  the  same  class.  What  I  affirms  as  also  true 
of  some  individuals  of  a  given  class,  O  denies,  not  of  all,  or 
of  the  same,  but  of  some  individuals  of  the  same  class.  From 
the  nature  of  this  opposition,  therefore,  the  following  rules  or 
axioms  obtain : 

1 .  If  one  universal  is  true,  its  opposite  universal  must  be  false 
If  "Every  A  is  B,"  the  proposition,  "No  A  is  B,"  must  be  false 
throughout. 

2.  The  fact  that  one  universal  is  false,  does  not  imply  that 
the  opposite  is  true.  The  propositions,  "  Every  A  is  B,"  and 
"  No  A  is  B,"  may  both  be  false,  and  each  of  the  particulars,  to 
wit :  "  Some  of  A  is  B,"  and  "  Some  of  A  is  not  B,"  may  be 
true.  The  propositions,  "  All  men  are  bars,"  and  "  No  men  are 
liars,"  are,  in  fact,  both  false ;  and  their  respective  particulars,, 
"  Some  men  are  liars,"  and  "  Some  men  are  not  liars,"  are  true. 

3.  If  either  particular  is  true,  its  opposite  universal  is  false. 
If  the  proposition,  "  Some  men  are  liars,"  is  true,  the  proposi- 
tion, "  No  men  are  liars,"  must  be  false.  So  in  all  other  in- 
stances. 

4.  The  fact  that  one  particular  is  true,  does  not  imply  that 
the  opposite  one  is  falsa.  Both  may  be,  and  often  are,  true. 
The  propositions,  "  Some  men  are  virtuous,"  and  "  Some  men 
are  not  virtuous,"  are  both  true. 

5.  If  a  universal  is  false,  its  opposite  particular  must  be  true ; 
and  if  the  particular  is  false,  its  opposite  universal  must  be  true. 
If  the  proposition,  "  No  A  is  B,"  is  false,  the  proposition,  "  Some 


A  is  B,"  must  be  true.  So  if  the  proposition,  "  Some  'A  is  B," 
is  false,  the  proposition,  "  No  A  is  B,"  must  be  true. 

6.  Both  particulars  can,  in  no  case,  be  false,  because  both  uni- 
versals  would  then  be  true,  which,  as  we  have  seen,  is  impos- 
sible. 

The  above  principles  will  be  found  to  be  of  very  great  impor- 
tance, when  understood  and  duly  reflected  on.* 

Of  the  Conversion  of  Propositions. 

A  proposition  is  said  to  be  converted  when,  without  a  change 
of  quality,  its  terms  are  transposed;  that  is,  the  subject  is  made 
the  predicate,  and  the  predicate  the  subject.  When  nothing 
more  is  done,  we  have  what  is  called  simple  conversion.  The 
original  proposition  is  called  the  exposita  /  when  converted,  it 
is  denominated  the  converse. 

Conversion  is  valid  when,  and  only  when,  nothing  is  asserted 
in  the  converse  which  is  not  affirmed  or  implied  in  the  exposita. 
Hence  the  universal  rule  of  conversion,  to  wit :  "  no  term  must 
be  distributed  in  the  converse  which  was  not  distributed  in  the 
expositaP  Whenever  this  is  done,  that  is  affirmed  of  the  whole 
class  which  was  before  only  asserted  of  a  part  of  it ;  that  is, 
more  is  affirmed  in  the  converse  than  was  implied  in  the  exposi- 
ta. The  following  are  the  necessary  applications  of  this  law  : 
.  1.  E  distributes  both  terms,  and  I  neither.  Each  of  these 
classes  of  propositions  may  always  be  converted  simply,  and  the 
conversion  will  be  illative  /  that  is,  the  truth  of  the  converse  is 
implied  in  the  truth  of  the  exposita.  If  the  proposition  in  E, 
"  No  virtuous  man  is  a  rebel,"  is  true,  its  converse,  "  No  rebel 
is  a  virtuous  man,"  must  be  true  also.  If  the  proposition  in  I, 
"  Some  boasters  are  cowards,"  is  true,  its  converse,  "  Some 
cowards  are  boasters,"  must  also  be  true. 

2.  A,  the  universal  affirmative,  distributes  only  the  subject.f 

*  See  Tappan's  Logic,  pp.  318-320,  where  most  of  the  above  principles  are  stated  and 
elucidated  with  great  precision  and  clearness. 

t  This  proposition,  as  we  shall  see,  holds  when,  and  only  when,  the  subject  represents  an 
Inferior  and  the  predicate  a  superior  conception. 


PROPOSITIONS.  83 

Its  simple  -conversion,  therefore,  would  not  be  illative.  From 
the  fact,  that  "All  men  are  mortal,"  we  cannot  infer,  or  affirm, 
that  all  mortal  beings  are  men.  That  fact  being  admitted, 
however,  we  can  affirm,  as  necessarily  implied  in  it,  the  truth  of 
the  proposition,  that  "  Some  mortal  beings  are  men."  Universal 
affirmatives,  then,  may  always  be  converted  by  making  the  con- 
verse particular  instead  of  universal.  This  has  been  denominated 
"conversion  by  limitation,"  or  "per  accident."  As  we  are  al- 
ways permitted  to  affirm  a  particular,  when  a  universal  might  be 
affirmed,  the  universal  negative  E  can  always  be  thus  converted. 

3.  The  particular  negative  distributes  the  predicate  instead 
of  the  subject.  Such  propositions,  therefore,  cannot  be  con- 
verted simply ;  since,  in  that  case,  we  should  have  the  predicate 
distributed  in  the  converse,  when  it  was  not  distributed  in  ex- 
posita.  As  Professor  Tappan  has  observed  :  "  According  to  a 
strict  exposition  of  the  form,  a  particular  negative  has  no  con- 
verse." From  the  fact,  "  That  some  men  are  not  truthful,"  we 
cannot  affirm,  that  "  Some  truthful  persons  are  not  men."  The 
proposition  is,  hi  fact,  incapable,  as  it  stands,  of  conversion.  It 
can  be  converted  only  by  changing  its  form  from  a  negative  to 
a  positive  ;  that  is,  by  attaching  the  term  of  negation  to  the 
predicate  of  the  exposita.  Take,  for  example,  the  proposition, 
"  Some  men  are  not  truthful."  From  such  a  proposition,  we 
may  affirm,  that  "  Some  persons  who  are  not  truthful  are  men." 
This  has  been  named  conversion  by  negation.  Since,  as  Dr. 
Whately  remarks,  "  it  is  the  same  thing  to  affirm  some  attri- 
bute of  the  subject,  as  to  deny  the  absence  of  that  attribute," 
the  universal  affirmative  may  always  be  converted  in  the  same 
manner.  From  the  fact,  for  example,  that  "  Every  virtuous 
man  is  a  true  patriot,"  we  may  infer,  that  "  Every  one  who  is 
not  a  true  patriot,  is  not  a  virtuous  man,"  or,  "  None  but  true 
patriots  can  be  virtuous." 

Thus,  as  Dr.  "Whately  states,  "  in  one  of  these  three  ways, 
every  proposition  may  be  illatively  converted,  viz. :  E  and  I 
simply  ;  A  and  O  by  negation  ;  A  and  E  by  limitation." 

Hardly  any  department  of  logic  needs  to  be  more  thorough- 
ly studied  and  reflected  upon  than  the  department  we  have  just 


passed  over,  when  treating  of  the  laws  and  principles  of  opposi- 
tion and  conversion  of  propositions.  When  a  proposition  is  ad- 
mitted as  self-evident,  or  as  having  been  proved  true,  few  per- 
sons seem  to  know  what  use  to  make  of  it,  and  that  in  conse- 
quence of  not  perceiving  what  is  implied  in  it. 

Quantification  of  the  Predicate. 

What  we  have  said  hitherto  in  regard  to  propositions,  has 
been  based  on  the  assumption,  that  the  quantity  of  propositions 
depends  icholly  upon  the  relations  of  the  whole  predicate  to  the 
subject.  If  the  former  is  affirmed  or  denied  of  the  ichole  sub- 
ject, the  proposition  is  universal.  If  it  is  affirmed  or  denied 
only  of  apart  of  the  subject,  the  proposition  is  particular.  We 
have  said  nothing  (for  the  reason  that  logic,  with  the  exception 
about  to  be  .named,  has  hitherto  left  the  subject  untouched)  of 
the  quantity  of  propositions  so  far  as  the  predicate  is  concerned. 
TO  Sir  William  Hamilton  the  world  is  indebted  for  one  of  the 
most  important  attainments  in  this  science  which  has  been 
made  for  centuries,  to  wit :  in  the  quantification  of  the  predi- 
cate as  well  as  of  the  subject.  In  all  propositions  alike,  as  he 
maintains,  if  we  refer  to  the  judgment  itself,  that  is,  to  what  is 
really  thought  in  the  mind,  the  predicate  always  has  as  real  a 
quantity  as  the  subject ;  and  that,  if  we  refer  to  the  judgment, 
and  not  to  the  words  of  the  proposition  expressing  it,  conver- 
sion of  propositions  is  always  and  exclusively  simple,  the  sub- 
ject and  predicate  being  really,  in  all  instances,  definite  in  their 
meaning.  Why,  for  example,  is  the  converse  of  the  proposi- 
tion, "  All  men  are  animals,"  this  :  "  Some  animals  are  men  ?"• 
The  answer  commonly  given  is :  "  That  the  subject  and  not  the 
predicate  is  distributed  in  this  proposition."  This  is  true,  as  far 
as  the  mere  form  of  expression  is  concerned.  If  we  refer  to 
the  thought  in  the  mind,  however,  we  shall  find  that  the  reason 
is,  that,  in  the  exposita,  the  subject  is  universal,  and  the  predi- 
cate particular.  What  we  really  mean,  when  we  say,  "All 
men  are  animals,"  is  not,  that  all  men  are  any  kind  of  annuals, 
but  some  kind ;  rational,  for  example.  The  proposition  before 
us,  then,  is  really  universal  relative  to  the  subject,  and  particu- 


PROPOSITIONS.  85 

lar  relative  to  the  predicate.  Hence,  by  simple  conversion,  we 
have  the  converse,  "  Some  animals  are  men."  The  propositions, 
on  the  other  hand,  "  Men  are  rational  animals,"  and  "  All  trian- 
gles are  figures  bounded  by  three  straight  fines,"  are  universal 
in  both  particulars ;  and  their  converse  would  be,  not  "  Some, 
but  all  rational  animals  are  men,"  and  not  "  Some,  but  all 
figures  bounded  by  three  straight  lines  are  triangles."  The 
proposition,  "  Men  are  wine-manufacturing  and  wine-drinking 
animals,"  however,  is  particular  in  respect  to  the  subject,  and 
universal  in  respect  to  the  predicate ;  its  real  meaning  being, 
"  Some  men  are  the  only  animals  of  this  class  that  do  exist," 
and  its  converse,  "  All  wine-manufacturing  and  wine-drinking 
animals  are  men."  The  proposition,  finally,  "  Some  rational  be- 
ings are  animals,"  is  particular,  both  in  reference  to  subject  and 
predicate,  its  real  meaning  being,  "  Some  rational  beings  are 
some  (some  one  class  of)  animals,"  and  its  converse,  consequent- 
ly, "  Some  animals  are  rational  beings." 

In  negative  propositions  also,  there  is  the  same  quantification 
of  the  predicate  as  in  affirmative  ones.  In  the  proposition, 
for  example,  "  No  animal  is  immortal,"  the  subject  and  predi- 
cate are  both  universal ;  the  real  meaning  of  the  proposition  be- 
ing, "  Any  animal  is  not  any  one  immortal  being,"  and  its  con- 
verse, "  Any  immortal '  being  is  not  any  (any  one)  animal."  In 
the  proposition,  on  the  other  hand,  "  Money  is  not  all  that  is 
valuable,"  the  subject  is  universal,  and  the  predicate,  though 
universal  in  form,  is  particular  in  fact ;  that  is,  the  thought  which 
it  represents  is  particular.  The  converse,  "  All  that  is  valuable 
is  not  money,"  really  means,  "  Some  things  that  are  valuable 
are  not  money."  The  real  meaning  of  the  exposita,  then,  is, 
"All  of  money  that  exists,  is  not  some  valuable  things."  In 
the  proposition,  "  Some  currency  is  not  metal,"  the  subject  is 
particular,  and  the  predicate  universal,  its  real  meaning  being, 
that  "  Some  one  kind  of  currency  is  not  any  kind  of  metal."  In 
the  proposition,  finally,  "  Some  men  are  not  like  other  men," 
both  the  subject  and  predicate  are  particular,  the  real  meaning 
being,  "  Some  individuals  of  a  class  are  not  like  others  of  a  given 
class."     So  the  proposition,  "  Some  qualities  of  some  individuals 


are  not  like  other  qualities  of  the  same  individual,"  is  equiva- 
lent to  the  proposition,  "  Some  of  A  (the  quality  B)  is  not  some 
of  A  (the  quality  C)." 

Rightly  classified,  then,  we  have  eight  instead  of  four  classes 
(A,  E,  I,  0)  of  propositions,  as  far  as  quantity  is  concerned,  to 
wit :  four  classes  of  affirmative,  and  four  of  negative,  proposi- 
tions.    Of  the  affirmative  we  have  : 

1st.)  The  "Toto-total=A  f  a,"  those  in  which  hoth  the  sub- 
ject and  predicate  are  universal,  as  to  quality ="  All  A  is  all 
of  B."  "  (All)  triangles  are  (include  all)  figures  bounded  by 
three  straight  lines." 

2d.)  The  "  Toto-partial=A-  f  i," — the  universal  affirmative 
recognized  by  logicians, — those  propositions  in  which  the  sub- 
ject is  universal,  and  the  predicate  particular,  "All  men  are 
mortal  (some  mortal  beings)"  =  "  All  A  is  some  B." 

3d.)  The  "  Parti-total = I  f  a"  =  "  Some  A  is  all  of  B." 

4th.)  The  "  Parti-partial = I  f  i"  =  "Some  A  is  B,"  that  is, 
some  B — the  particular  affirmative  of  logicians. 

Of  negative  propositions,  we  have  : 

5th.)  The  "Toto-total=A  n  a" ="  Any  is  not  any" ="  Any 
man  is  not  any  irrational  animal."  This  is  E — the  universal 
negative  of  logicians. 

6th.)  "Toto-partial:=A  n  i"="Any  is  not  some" ="  All  of 
A  is  not  B,"  that  is,  some  of  B.  "All  of  money  is  not  all  of 
valuable  things,"  that  is,  some  valuable  things. 

7th.)  "  Parti-total = I  n  a"="Some  is  not  any"="Some  A 
is  not  B,"  that  is,  any  part  of  B.  "  Some  currency  is  not 
coin,"  that  is,  any  coin.  This  is  the  particular  negative  of  logi- 
cians. 

8tb.)  "  Parti-partial = I  n  i"  =  "Some— is  not  some,"  that  is, 
"Some  of  A  (B)  is  not  some  of  A  (C)."  "Some  men  are  not 
like  some  other  men." 

This  formula,  though  hitherto,  as  Sir  William  Hamilton  af- 
firms, "  totally  overlooked  by  logicians,  is  one  of  the  most  im- 
portant and  commonly  used  of  all  the  others.  It  lies,  indeed, 
at  the  basis  of  all  the  processes  of  specification  and  individuali- 
zation, that  is,  the  process  by  which  a  class  (genus  or  species)  is 


PROPOSITIONS.  87 

divided  into  its  subject-parts,  the  counter-process,  to  wit:  of 
quantification."  We  have  before  us,  for  example,  a  certain  class 
of  objects,  we  immediately  begin  to  separate  them  into  distinct 
sub-classes,  and  these  last  we  individualize,  separate,  and  distin- 
guish as  individuals.  How  is  this  done  ?  It  is  wholly  based 
upon  the  perception  (judgment),  that  some  portions  of  the  class 
first  named  differ  from  some  other  portions  of  the  same  class  ; 
that  is,  upon  the  judgment,  that  "  Some  A  is  not  some  A."  In 
the  sub-classes,  we  may  find,  by  means  of  the  same  formula, 
other  specific  differences,  and  thus  continue  the  process  till  we 
have  arrived  at  the  lowest  species.  This  last  is  individualized, 
as  above  stated.  On  the  same  principle,  the  qualities  of  the  in- 
dividual are  separated  from  each  other,  till  we  come  to  elements 
incapable  of  division — the  contradictory  of  the  proposition- - 
"  Some  is  not  some" — being  the  affirmation  of  absolute  indi- 
viduality, or  indivisibility.  For  the  sake  of  perspicuity  and  elu- 
cidation, as  well  as  to  bring  out  more  fully  the  true  aims  of 
logic  itself,  we  now  give  the  following  lengthy  extract  from  Sir 
William  Hamilton,  an  extract  containing  an  objection  to  the 
formula  under  consideration,  and  the  author's  reply  to  the  same. 

"  Parti-partial  Negation. 

"To  this  Mr.  do  Morgan  makes  the  following  objection  : 
" '  Thirdly,  the  proposition,  "  Some  X's  are  not  some  F~'s," 
has  no  fundamental  proposition  which  denies  it,  and  not  even  a 
compound  of  other  propositions.  It  is  then  open  to  the  above 
objection  ;  and  to  others  peculiar  to  itself.  It  is  what  I  have 
called  (F,  L,  p.  153)  a  spurious  proposition,  as  long  as  either  of 
its  names  applies  to  more  than  one  instance.  And  the  denial 
is  as  follows :  "  There  is  but  one  A",  and  but  one  F,  and  X 
is  Y."  Unless  we  know  beforehand,  that  there  is  but  one  sol- 
dier, and  one  animal,  and  that  soldier  the  animal,  we  cannot 
deny  "  that  some  soldiers  are  not  some  animals.''''  When- 
ever we  know  enough  of  X  and  Y  to  bring  forward  "  some 
X's  are  not  some  F~'s,"  as  what  could  be  conceived  to  have 
been  false,  we  know  more,  namely,  "  no  X  is  F,"  which,  when 


88  LOGIC. 

X  and  Y  are  singular,  is  true  or  false  with  "some  X's  are 
not  some  Y's.' " 

"  Here,  also,  Mr.  de  Morgan  wholly  misunderstands  the  na- 
ture and  purport  of  the  form  which  he  professes  to  criticise. 
He  calls  it  '  a  spurious  proposition.'  /Spurious,  in  law,  means  a 
bad  kind  of  bastard.  This  is,  however,  not  only  a  legitimate, 
for  it  expresses  one  of  the  eight  necessary  relations  of  proposi- 
tion al  terms,  but,  within  its  proper  sphere,  one  of  the  most  impor- 
tant of  the  forms  which  logic  comprehends,  and  which  logicians 
have  neglected.  It  may,  indeed,  and  that  easily,  be  illogically 
perverted.  It  may  be  misemployed  to  perform  the  function 
which  other  forms  are  peculiarly  adapted  more  effectually  to 
discharge ;  it  may  be  twisted  to  sever  part  of  one  notion  from 
part  of  another,  the  two  total  notions  being  already,  perhaps, 
thought  as  distinct ; — and  then,  certainly,  in  this  relation,  it 
may  be  considered  as  useless ; — but  in  no  relation  can  it  ever 
logically  be  denominated  ' spurious.''  For  why?  Whatever 
is  operative  in  thought,  must  be  taken  into  account,  and,  con- 
sequently, be  overtly  expressible  in  logic ;  for  logic  must  be, 
as  it  professes  to  be,  an  unexclusive  reflex  of  thought,  and 
not  merely  an  arbitrary  selection — a  series  of  elegant  extracts, 
out  of  the  forms  of  thinking.  Whether  the  form  that  it  ex- 
hibits as  legitimate,  be  stronger  or  weaker,  be  more  or  less 
frequently  applied ; — that,  as  a  material  and  contingent  con- 
sideration, is  beyond  its  purview.  But,  the  form  in  question 
is,  as  said,  not  only  legitimate — not  '  spurious' — it  is  most  im- 
portant. 

"  What  then  is  the  function  which  this  form  is  peculiarly — 
is,  indeed,  alone,  competent  to  perform  ?  A  parti-partial  nega- 
tive is  the  proposition  in  which,  and  in  which  exclusively,  we  de- 
clare a  whole  of  any  kind  to  be  divisible.  '  Some  A  is  not 
some  A,' — this  is  the  judgment  of  divisibility  and  of  division ; 
the  negation  of  this  judgment  (and  of  its  corresponding  inte- 
grant) in  the  assertion,  that  "  A  has  no  some,  no  parts,"  is  the 
judgment  of  indivisibility,  of  unity,  of  simplicity.  This  form  is 
implicitly  at  work  in  all  the  sciences,  and  it  has  only  failed  in 
securing  the  attention  of  logicians,  as  an  abstract  form,  because, 


PROPOSITIONS.  89 

in  actual  use,  it  is  too  familiar  to  be  notorious,  lying,  in  fact, 
unexpressed  and  latescent  in  every  concrete  application.  Even 
in  logic  itself,  it  is  indispensable.  In  tbat  science  it  constitutes 
no  less  than  the  peculiar  formula  of  the  great  principle  of  speci- 
fication (and  individualization),  that  is,  the  process  by  which 
a  class  (genus  or  species)  is  divided  into  its  subject-parts — the 
counter-process,  to  wit,  of  generification.  And  this  great  logi- 
cal formula  is  to  be  branded  by  logical  writers  as  '  spurious  !' 
No  doubt,  the  particularity,  as  a  quantity  easily  understood,  is 
very  generally  elided  in  expression,  though  at  work  in  thought ; 
or  it  is  denoted  by  a  substitute.  Meaning,  we  avoid  saying — 
'  Some  men  are  not  some  men.'  This  we  change,  perhaps,  into 
'men  are  not  men,'  or  'how  different  are  men  from  men,'  or 
'  man  from  man,'  or  '  these  from  those,'  or  '  some  from  other,' 
&c.  Still,  '  some  is  not  some,'  lies  at  the  root ;  and,  when  we 
oppose  '  other,'  '  some  other,'  &c,  to  '  some,'  it  is  evident,  that 
'  other'  is  itself  only  obtained  as  the  result  of  the  negation, 
which,  in  fact,  it  pleonastically  embodies.  For  '  other  than'  is 
only  a  synonym  for  '  is  not ;'  '  other  (or  some  other)  A,'  is  con- 
vertible with  '  not  some  A ;'  while"  there  is  implied  by  '  this,' 
'  not  that ;'  by  '  that,'  '  not  this  ;'  and  by  '  the  other,'  '  neither 
this  nor  that ;'  and  so  on.  Here  we  must  not  confound  the 
logical  with  the  rhetorical,  the  necessary  in  thought  with  the 
agreeable  in  expression. 

"  Following  Mr.  de  Morgan,  in  his  selected  example,  and  not 
even  transcending  his  more  peculiar  science,  in  the  first  place, 
as  the  instance  of  division,  I  borrow  his  logical  illustration  from 
the  class  '  soldier.'  Now  in  what  manner  is  the  generic  notion 
divided  into  species  ?  We  say  to  ourselves  :  '  Some  soldier  is 
not  some  soldier,'  for  '  some  soldier  is  (all)  infantry ;  some  sol- 
dier is  (all)  cavalry,'  &c,  and  '  (any)  infantry  is  not  any  caval- 
ry.' A  parti-partial  negative  is  the  only  form  of  judgment  for 
division,  of  what  kind  soever  be  the  whole  (and  Mr.  de  Morgan 
can  state  for  it  no  other).  Again  :  in  the  second  place,  as  the 
example  of  indivisibility :  '  Some  of  this  point  is  not  some  of 
this  (same)  point.'  Such  a  proposition,  Mr.  de  Morgan,  as  a 
mathematician,  cannot  admit ;   for  a  mathematical  point  is,  ex 


hypothesis  'without  some — without  some,  and  some1 — without 
parts,  same,  and  other  ;  it  is  indivisible.  He  says,  indeed,  that 
a  parti-partial  negative  cannot  be  denied.  But  if  he  be  unable 
to  admit,  he  must  be  able  to  deny  ;  and  it  would  be  a  curious — 
a  singular  anomaly,  if  logic  offered  no  competent  form  for  so  or- 
dinary a  negation ;  if  we  could  not  logically  deny  that  /Socrates 
is  a  class — that  an  individual  is  a  universal — that  the  thought 
of  an  indivisible  unit  is  the  thought  of  a  divisible  plurality?'' 

Criteria  by  which  Propositions  properly  falling  under  these 
different  classes  may  be  distinguished  from  each  other. 

We  will  now  attempt  to  give,  what  our  author  has  not 
formally  done,  special  criteria,  by  which  we  may  distinguish 
propositions  which  fall  under  these  different  classes  from  one 
another.  The  following,  we  think,  will  be  admitted  as  univer- 
sally valid,  as  such  criteria  : 

1.  When  the  object  of  the  proposition  is  to  give  a  correct  and 
full  definition  of  a  term  or  subject — or  to  assert  the  essential 
characteristics  of  an  individual  or  class — or  finally,  to  assert  a 
real  and  perfect  identity  between  the  subject  and  predicate, 
then  the  proposition  is  to  be  classed  as  toto-total  affirmative. 
Thus,  in  the  definition,  "  A  triangle  is  a  figure  bounded  by  three 
straight  lines,"  we  mean,  all  triangles  include  all  such  figures. 
So  in  all  full  definitions.  When,  on  the  other  hand,  we  affirm 
that  "  All  equilateral  triangles  are  equiangular,"  the  predicate 
represents  a  characteristic  conception  of  the*  subject.  Of  course, 
it  is  found  only  in  the  subject,  and  always  found  in  it.  The  sub- 
ject and  predicate,  therefore,  stand  related ;  as,  "All  A  is  all  of 
B."  Of  the  same  character  is  the  proposition,  "  A  good  gov- 
ernment is  one  that  has  the  "good  of  its  subjects  as  its  object." 
When  we  say,  finally,  "  A  Christian  is  a  man  who  fears  God," 
we  mean  that  there  is  a  real  identity  between  the  subject  and 
predicate  in  this  case.  The  proposition,  therefore,  like  those 
before  mentioned,  is  equivalent  to  "  All  A  is  all  of  B."  The 
converse  of  all  such  propositions,  consequently,  is  a  universal 
affirmative. 


PROPOSITIONS.  91 

2.  When  the  judgment  really  affirmed  in  a  proposition  is, 
that  individuals  belong  to  a  certain  class,  as,  "  John  is  a  man," 
or  that  all  the  individuals  represented  by  an  inferior  conception 
rank  specifically  under  a  superior  conception,  as,  "All  men  are 
animals,"  "All  men  are  mortal,"  &c,  then  the  proposition  is 
"  toto-partial,"  the  universal  affirmative  of  logicians ;  that  is,  the 
subject  is  universal  and  the  predicate  particular ;  and  the  con- 
verse is  a  particular  affirmative,  "  Some  man  is  John,"  "  Some 
mortal  beings  are  men,"  &c. 

3.  When  the  judgment  affirmed  in  a  proposition  is,  that  a  qual- 
ity assumed  as  attaching  exclusively  to  a  certain  class,  but  not  to 
all  the  members  thereof,  belongs  exclusively  to  that  class — as, 
"  Men  possess  wealth  ;"  or,  that  a  superior  conception  embraces 
under  it  all  the  individuals  included  under  an  inferior  one — as, 
"  Some  animals  are  men,"  "  A  part  of  currency  is  gold  coin," 
then  the  proposition  is  parti-total,  the  exposita  being,  "  Some 
men  possess  all  of  wealth,"  "  Some  part  of  currency  is  all  of 
gold  coin,"  &o. ;  and  the  converse  a  toto-partial  affirmative,  to 
wit:  "All  of  wealth  is  possessed  by  men  (some  men),"  "All 
gold  coin  is  currency  (some  part  of  currency)." 

4.  When  the  judgment  affirmed  in  a  proposition  is,  that  some, 
not  all,  individuals  of  one  class  are  like  some,  not  all,  individuals 
of  another,  as,  "  Some  men  are  long-lived  animals,"  then  the 
proposition  is  a  parti-partial  affirmative,  and  its  converse  of  the 
same  class,  "  Some  long-lived  animals  are  men." 

5.  When  the  judgment  affirmed  in  a  proposition  is  this, 
that  no  individual  of  one  class  is  a  member  of  another  class, 
"  No  man  is  an  angel ;"  or,  that  a  certain  individual  is  utterly 
void  of  given  characteristics  or  class  of  characteristics,  "  John 
possesses  no  virtue  ;"  or,  that  a  certain  individual  does  not  be- 
long to  a  certain  class,  "  A  is  not  an  American,"  then  the  prop- 
osition is  a  toto-total  negative,  and  its  converse  will  be  of  the 
same  character ;  as,  "  No  angel  is  a  man  (any  man),"  "  No  vir- 
tue attaches  to  John,"  "  No  American  is  A,"  &c. 

6.  When  one  conception  is  admitted  to  represent  all  that 
another  does,  and  some  other  things  besides,  and  when  the  ob- 
ject of  the  proposition  is  to  deny  that  what  is  embraced  in  the 


92  LOGIC. 

former  includes  all  that  is  embraced  in  the  latter — as,  "  All  of 
A  is  not  all  of  B,"  that  is,  some  of  B — then  the  proposition  is  a 
toto-partial  negative ;  and  its  converse  a  parti-total  negative, 
"  Some  B  is  not  A  (any  of  A)".  So  when  the  object  of  a  prop- 
osition is  to  deny  of  an  individual  the  totality  of  characteristics 
represented  by  a  given  conception ;  as,  "  A  has  not  all  the 
vices,"  that  is,  some  vices. 

7.  When  the  judgment  affirmed  in  a  given  proposition  de- 
nies that  some  individuals  of  a  given  class  have  any  of  the  char- 
acteristics belonging  to  other  individuals  of  the  same  class,  or 
to  any  individual  of  another  class — as,  "  Some  members  of  the 
university  are  not  studious,"  "  Some  Americans  are  not  pa- 
triots," &c. ;  or,  that  all  the  individuals  embraced  under  a  supe- 
rior conception  are  found  among  those  embraced  under  an  infe- 
rior one — as,  "  Some  animals  are  not  brutes ;"  the  proposition 
is  then  parti-total,  and  its  real  converse  would  be  a  toto-partial 
negative,  "  All  A  is  not  some  of  B  :"  a  certain  class  of  studious 
persons  does  not  include  some  members  of  the  university,  or 
any  studious  person  is  not  some  member  of  the  university. 

8.  When  the  judgment  affirmed  in  a  given  proposition  de- 
nies the  absolute  indivisibility  of  any  object,  or  the  absolute 
likeness  of  all  its  qualities  to  one  another — as,  "  Some  A  (the 
quality  B)  is  not  some  A  (the  quality  C)  ;"  or,  that  some  mem- 
bers of  a  given  class  are  not  like  other  members  of  the  same 
class — as,  "  Some  men  are  not  men,"  that  is,  do  not  belong  to 
the  class  who  properly  represent  humanity ;  then  the  proposi- 
tion is  a  parti-partial  negative,  and  its  converse  the  same. 

Such  are  the  principles  of  classification  of  propositions,  when 
respect  is  had  to  their  sense,  and  not  to  the  mere  language  m 
which  the  sense  is  expressed.  The  rules  presented  in  the  pre- 
ceding section  are  applicable,  when  reference  is  had,  not  to  the 
sense  exclusively,  but  to  the  mere  words  of  the  propositions 
themselves. 

Scholia  1.  The  most  philosophical  or  scientific  classification 
of  propositions  would  be,  as  Sir  William  Hamilton  observes,  into 
two  classes — the  definite  and  indefinite.  All  universal  and  all 
individual  propositions  are  definite,  affinning  or  denying  in  re- 


PROPOSITIONS.  93 

gard  to  each  and  every  individual  referred  to.  The  terms, 
"  John,  any  man,  no  man,"  &c.,  are  each  alike  and  equally  defi- 
nite. The  term,  "Some  (some  men),"  is  indefinite.  So  the 
propositions,  "  John  is  an  American,"  "  Every  man  is  mortal," 
"  No  man  is  a  brute,"  &c,  are  each  and  all  alike  definite  propo- 
sitions ;  while  the  proposition,  "  Some  men  are  learned,"  is  in- 
definite. As  all  propositions  are  either  individual,  universal,  or 
particular,  and  as  the  two  classes  first  named  are  definite,  and 
the  latter  class  indefinite,  all  propositions,  if  strict  scientific  pre- 
cision were  observed,  would  be  classed  as  definite  or  indefinite. 

Scholia  2.  Propositions  whose  subject  and  predicate  are  both 
definite,  may  properly  be  called  definite-definite  ;  those  whose 
subject  and  predicate  are  both  indefinite,  might  be  called  indefi- 
nite-indefinite propositions ;  those  whose  subject  is  universal 
and  predicate  particular,  the  definite-indefinite ;  and,  finally, 
those  whose  subject  is  particular  and  predicate  universal,  the 
indefinite-definite.  We  thus  have  a  complete  and  exhaustive 
system  of  classifying  propositions. 

Scholia  3.  All  conversion  of  propositions  in  accordance  with 
the  most  perfect  scientific  procedure,  is,  as  Sir  William  Hamil- 
ton has  affirmed,  exclusively  simple.  Example  :  "  All  men  are 
mortal."  Why  is  the  converse  of  this  proposition  this,  "  Some 
mortal  beings  are  men  ?"  The  reason  is  obvious,  the  subject  of 
the  exposita  is,  in  fact,  universal,  while  the  predicate  is  particu- 
lar. The  converse,  on  the  other  hand,  as  thought,  is  parti-total, 
to  wit :  "  Some  mortal  beings  are  all  of  mankind."  Hence,  we 
have  in  reality,  if  we  refer,  not  to  the  form,  but  to  the  matter 
of  the  judgment,  that  is,  to  what  is  given  in  the  thought,  but 
one  form  of  conversion,  that  is,  simple.  Unless  this  principle  is 
kept  distinctly  in  mind,  logic,  as  a  science,  will  not  be  under- 
stood. 


CHAPTER  III. 

ANALYTIC  OF  ARGUMENTS  OR  SYLLOGISMS. 
Section  I. — Abgument  defined  and  elucidated. 

An  argument  is  an  intellectual  process  in  which  one  judg- 
ment is  deduced  from  another.  All  judgments  are  either  intui- 
tive or  inferential,  immediate  or  mediate.  When  the  relation 
between  two  objects  or  conceptions  is  such,  that  the  mind  has, 
from  the  nature  of  said  relation,  a  direct  and  immediate  percep- 
tion of  the  same,  the  judgment  affirming  such  relation  is  called 
intuitive  or  immediate.  When,  on  the  other  hand,  this  relation 
is  discerned  through  other  judgments,  the  judgments  affirming 
such  relation  is  said  to  be  inferential  or  mediate. 

The  characteristics  of  all  valid  immediate  or  intuitive  judg- 
ments have  already  been  given.  When  the  relations  between 
any  two  objects  or  conceptions,  A  and  B,  are  not  immediately 
discernible,  it  is  self-evident  that  such  relations  can  be  discerned 
but  upon  one  condition — that  each  of  those  objects  sustain 
known  or  knowable  relations  to  some  one  known  object,  C. 
Through  their  discerned  relations  to  this  known  object,  we  may 
infer  (discern)  their  relations  to  each  other.  Thus,  if  A  and  B 
are  both  equal  to  C,  we  infer  that  they  must  be  equal  to  each 
other.  If,  on  the  other  hand,  one  agrees  and  the  other  disa- 
grees with  C,  we  infer  that  they  must  disagree  with  each  other. 
On  this  principle,  exclusively,  all  mediate  judgments  are  de- 
duced. 

The  term  C,  with  which  the  others  are  compared,  is  called 
the  middle  term.  Those  compared  with  it  (A  and  B),  are  called 
the  extremes.     Hence  we  remark  : 

1.  That  in  no  given  argument  can  there  be  more  than  one 
middle  term.  If  there  was,  then  the  extremes  would  not  be 
compared  with  the  same  thing,  and  nothing  pertaining  to  their 
relations  to  each  other  could  be  inferred  from  the  comparison. 


ANALYTIC     OP     SYLLOGISMS.  95 

2.  In  such  argument  there  must  be  two  extremes,  and  there 
can  be  no  more.  If  there  were  more  than  two,  there  would  be 
a  corresponding  number  of  distinct  arguments. 

3.  There  must  be,  in  such  argument,  when  stated  at  length 
and  in  full,  three,  and  no  more,  and  no  less,  propositions :  two 
called  premises,  hi  one  of  which,  one,  and  in  the  other  the  re- 
maining extreme,  is  compared  with  the  middle  term,  and  the 
conclusion  or  inference  in  which  the  relation  of  the  two  terms 
is  affirmed.  The  truth  of  this  statement  is  too  evident  to  need 
any  further  elucidation. 

Note. — The  subject  of  the  conclusion  is,  in  logics  generally, 
called  the  minor  term,  and  the  predicate  of  the  conclusion  the 
major  term.  The  premise  in  which  the  minor  term  is  compared 
with  the  middle,  is  called  the  minor  premise,  and  that  in  Avhich 
the  major  term  is  compared  with  the  middle,  is  called  the  ma- 
jor premise. 

4.  When  each  premise,  together  with  the  conclusion,  is  stated 
in  its  proper  form  and  order,  the  argument  is  then  called  a  syl- 
logism ;  and  this  is  what  is  meant  by  the  term  syllogism.    For 

example : 

Every  C  is  B  ; 

Every  A  is  C  ; 

<*  .-.  Every  A  is  B. 

5.  From  the  nature  of  the  syllogism,  as  above  denned  and 
elucidated,  it  is  manifest  that  the  following  is,  and  must  be,  the 
universal  canon  or  principle  in  conformity  to  which  all  valid 
conclusions  must  be  deduced,  namely  :  All  conceptions  or  terms 
which  agree  with  one  and  the  same  third  conception  or  term, 
agree  with  each  other,  and  any  two  conceptions  or  terms,  the 
one  agreeing  and  the  other  disagreeing  with  said  common  con- 
ception or  term,  disagree  with  each  other.  The  validity  of  this 
principle  is  self-evident.  All  forms,  also,  which  the  syllogism 
can  assume  grow  out  of  the  diversified  applications  of  this  one 
principle ;  and  the  principle  itself,  always  one  and  identical, 
assumes  different  forms  according  to  the  nature  of  the  relations 
to  which  it  is  applied. 

*  The  6ign  (.*.)  will  be  U6ed  to  designate  the  term  "  therefore,"  or,  the  conclusion. 


DIVERSE   FORMS    OF   THE    SYLLOGISM. 

The  syllogism  assumes  diverse  forms,  each  of  which  demands 
especial  elucidation.  Among  these  we  notice  in  this  connec- 
tion the  following : 

Section  II. — The  Analytic  and  Synthetic  Syllogism. 

When  the  conclusion  (more  properly  the  theorem  or  propo- 
sition to  be  proved)  is  stated  first,  and  the  propositions  by 
which  it  is  to  be  proven  are  subsequently  stated,  the  syllogism 
is  said  to  be  analytic.     For  example  : 

Every  A  is  B 

Because,  Every  C  is  B 

And,  Every  A  is  C 

"  Caesar  was  a  usurper,"  because,  perforce,  he  seized  the  reins 
of  government  in  Rome,  and  every  one  who  does  this  is  a 
usurper.  On  the  other  hand,  when  the  premises  are  stated  first 
in  their  proper  order,  and  the  conclusion  last,  the  syllogism  is 
then  called  synthetic.    For  example : 

Every  C  is  B  ; 

Every  A  is  C  ; 

.-.  Every  A  is  B. 

Every  one  who  forcibly  seizes  the  reins  of  government  is  a 
usurper.  Caesar  did  this.  Therefore,  "  Caesar  was  a  usurper." 
The  following  observations  will  sufficiently  elucidate  the  nature 
and  relations  of  these  two  distinct  forms  of  the  syllogism  : 

These  distinct  forms  of  the  Syllogism  elucidated. 

1.  They  differ  not  at  all  in  thotight,  but  only  in  form.  A 
mere  inspection  of  the  two  forms  of  syllogisms,  as  given  above, 
will  render  this  statement  self-evident.  Each  form  consequent- 
ly is  equally  valid. 

2.  The  analytic  is  the  most  common  and  natural  form  of  the 
syllogism,  it  being  a  far  more  common  procedure  in  reasoning 


ANALYTIC     OF     SYLLOGISMS.  97 

to  state  first  the  proposition  to  be  proved  (conclusion  or  thesis), 
and  then  to  present  the  evidence  of  its  truth,  than  it  is  to  take 
the  opposite  course. 

3.  "In  point  of  fact,"  to  quote  the  language  of  Sir  William 
Hamilton,  to  Avhom  we  would  very  gratefully  acknowledge  our- 
selves indebted  for  the  above .  distinction,  "  the  analytic  syllo- 
gism is  not  only  the  more  natural,  it  is  even  presupposed  by 
the  synthetic.  To  express  in  words,  we  must  analyze  in  thought 
the  organic  whole — the  mental  simultaneity  of  a  simple  reason- 
ing ;  and  then  we  may  reverse  in  thought  the  process,  by  a  syn- 
thetic return.  Further,  we  may  now  enounce  the  reasoning 
in  either  order  ;  but,  certainly  to  express  it  in  the  essential,  pri- 
mary, or  analytic  order,  is  not  only  more  natural,  but  more 
direct  and  simple,  than  to  express  it  in  the  accidental,  seconda- 
ry, or  synthetic." 

4.  The  following  citation  from  the  same  author  wall  still  fur- 
ther elucidate  the  importance  of  the  distinction  under  consider- 
ation : 

"  This  in  the  first  place  relieves  the  syllogism  of  two  one- 
sided views.  The  Aristotelic  syllogism  is  exclusively  synthetic  ; 
the  Epicurean  (or  Neocletian)  syllogism  was — for  it  has  been 
long  forgotten — exclusively  analytic ;  while  the  Hindoo  syllo- 
gism is  merely  a  clumsy  agglutination  of  these  counter-forms, 
being  nothing  but  an  operose  repetition  of  the  same  reasoning, 
enounced,  1st.  Analytically ;  2d.  Synthetically.  In  thought 
the  syllogism  is  organically  one  ;  and  it  is  only  stated  in  an 
analytic  or  synthetic  form  from  the  necessity  of  adopting  the 
one  order  or  the  other,  in  accommodation  to  the  vehicle  of  its 
expression — language.  For  the  conditions  of  language  require 
that  a  reasoning  be  distinguished  into  parts,  and  these  detailed 
before  and  after  each  other.  The  analytic  and  synthetic  orders 
of  enouncement  are  thus  only  accidents  of  the  syllogistic  pro- 
cess. This  is,  indeed,  shown  in  practice  ;  for  our  best  reason- 
ings proceed  indifferently  in  either  order. 

"  In  the  second  place  this  central  view  vindicates  the  syllogism 
from  the  objection  ofpetitio  pri?icipii,  which  professing  logical- 
ly to  annul  logic,  or  at  least  to  reduce  it  to  an  idle  tautology, 


defines  syllogistic — the  art  of  avowing  in  the  conclusion  what 
has  been  already  confessed  in  the  premises.  This  objection 
(which  has  at  least  an  antiquity  of  three  centuries  and  a  half)  is 
only  applicable  to  the  synthetic  or  Aristotelic  order  of  enounce- 
ment,  which  the  objectors;  indeed,  contemplate  as  alone  possi- 
ble. It  does  not  hold  against  the  analytic  syllogism ;  it  does 
not  hold  against  the  syllogism  considered  aloof  from  the  acci- 
dent of  its  expression  ;  and  being  proved  irrelevant  to  these,  it 
is  easily  shown  in  reference  to  the  synthetic  syllogism  itself,  that 
it  applies1  only  to  an  accident  of  its  external  form."* 

5.  As  the  analytic  and  synthetic  syllogisms  differ  only  in 
form  and  are  identical  in  thought,  they  mutually  elucidate  each 
other.  Suppose  we  have  argued  the  ti'uth  of  some  proposition 
until  we  have,  as  we  suppose,  proved  it.  The  argument  has,  as 
is  almost  universally  the  case,  been  conducted  wholly  in  the 
analytic  form.  We  now  wish  to  test  the  validity  of  the  argu- 
ment. The  best  way  to  accomplish  this  will  be,  in  most  in- 
stances, to  change  the  form  from  the  analytic  to  the  synthetic, 
and  see  whether  the  premises  necessitate,  as  an  inference,  the' 
truth  of  the  proposition  affirmed  to  have  been  proven. 

6.  For  the  reasons  which  have  been  already  stated,  the  laws 
and  principles  which  govern  these  two  forms  of  the  syllogism 
are  one  and  identical.  "  Every  especial  variety  in  the  one,"  to 
use  the  language  of  the  author  above  referred  to,  "  has  its  cor- 
responding variety  in  the  other." 

7.  The  error,  we  remark  in  the  last  place,  of  modern  and 
most  of  the  ancient  logicians,  in  treating  the  synthetic  as  the 
only  and  exclusive  form  of  the  syllogism,  is  now  sufficiently  man- 
ifest and  no  additional  remarks  upon  the  subject  are  necessary. 

*  The  error  involved  in  the  above  objection,  even  in  its  application  to  the  synthetic  syllo- 
gism, may  be  made  manifest  by  a  single  illustration.    For  example  : 
Gold  is  precious ; 
This  substance  is  gold ; 
.'.  It  is  precious. 
It  is  very  true,  that  what  is  here  announced  in  the  conclusion,  is,  in  a  certain  form, 
fessed  in  the  premises.    The  object  of  the  syllogism,  however,  is  to  announce  in  form,  what 
has  previously  been  ascertained  by  investigation.    Suppose  the  conclusion  to  be  denied; 
tests  would  then  be  applied  to  verify  the  minor  premise.     When  its  truth  has  been  estab- 
lished, then,  and  not  till  then,  it  logically  takes  its  place  as  a  premise. 


ANALYTIC     OP     SYLLOGISMS. 


Section  III. — Figured  and  Unfigured  Syllogisms. 


Science  is  indebted  to  Sir  William  Hamilton  for  another  di- 
vision of  syllogisms  of  fundamental  importance  to  a  full  and  dis- 
tinct understanding  of  the  doctrine  of  the  syllogism  in  general, 
or  of  the  universal  process  of  reasoning.  We  refer  to  his  dis- 
tinction between  the  figured  and  unfigured  syllogism. 

In  the  figured  syllogism,  as  we  shall  see  hereafter,  the  terms 
compared  sustain  to  each  other,  in  the  several  propositions,  the 
relations  of  subject  and  predicate,  the  figure  of  the  syllogism  re- 
ferring to  the  situation  of  the  middle  term  in  the  premises  rela- 
tively to  the  extremes. 

In  the  unfigured  syllogism,  "  the  terms  compared  do  not 
stand  to  each  other  in  the  reciprocal  relation  of  subject  and 
predicate,  these  being  in  the  same  proposition,  on  the  other 
hand,  both  subject  and  predicate."     For  example  : 

All  C  and  some  B  are  equal  ; 
All  A  and  all  B  are  equal ; 
.-.  All  C  and  some  A  are  equal  ;  or, 
C  and  A  are  unequal. 

Again,  a  question  arises  whether  C  and  A  were  together  dur- 
ing the  whole  of  a  given  journey  taken  by  the  latter.  In  reply, 
it  is  affirmed,  that  from  sources  perfectly  reliable,  it  has  been 
ascertained  that  hi  the  journey  referred  to,  C  and  B  were  in 
company  only  part  of  the  distance  travelled  by  the  latter,  and 
that  from  sources  equally  reliable,  it  has  been  ascertained  that 
A  and  B  were  in  company  during  the  wJtole  distance  travelled 
by  each.  The  inference  is  hence  drawn  that  C  travelled  but 
a  part  of  the  distance  referred  to  in  company  with  A.  This 
conclusion  is  perfectly  valid,  and  the  form  of  argumentation 
by  which  it  is  reached  is  as  legitimate  as  any  other,  and 
withal  quite  as  worthy  to  be  elucidated  in  a  treatise  on  logic  ; 
and  that  for  the  obvious  reason  that  it  is  one  of  the  most  com- 
mon forms  of  reasoning  in  almost  all  departments  of  thought. 
Indeed,  logic,  as  a  science,  will  be  fundamentally  incomplete 
and  imperfect,  while  it  overlooks  this  one  form  of  the  syllogism. 


Without  further  remarks,  we  shall  now  proceed  to  elucidate 
some  of  the  laws  and  principles  of  the  unfigured  syllogism. 

PRINCIPLES   AND   LAWS    OF   THE   UNFIGURED   SYLLOGISM. 

The  Canon  of  this  Syllogism. 

The  canon  of  this  syllogism  we  give  in  the  language  of  the 
author  above  quoted  from.  "  In  as  far  as  two  notions  (notions 
proper  or  individuals)  either  both  agreeing,  or  one  agreeing, 
and  the  other  disagreeing,  with  a  common  third  notion :  just  so 
far  those  notions  do  or  do  not  agree  with  each  other."  Take 
the  following  examples  in  illustration : 

All  C  and  all  or  some  B  are  equal ; 
All  A  and  all  B  are  equal ; 
.-.  All  C  and  all  or  some  A  are  equal ; 
And  consequently,  C  and  A  are,  or  are  not,  equal  to  each  other. 
Again :  All  C  and  one-half  of  B  are  equal ', 
All  A  and  all  B  are  equal ; 
.•.  All  C  and  one-half  of  A  are  equal ;  or, 
C  equals  one-half  of  A. 
Again  :  A  to  B,  and  E  to  F,  are  in  the  same  proportional  relations  ; 
But,  E  is  three  times  F  ; 
.-.  A  is  three  times  B. 

If  the  minor  had  been  in  this  case,  A  is  three  times  B,  the 
conclusion  would  have  been,  that  E  is  three  times  F  ;  and  the 
former  couplet  might  as  properly  have  been  the  minor,  as  the 
latter.  Had  the  relation  above  named  been  that  of  analogy, 
the  argument  would  be  the  same. 

The  following  present  other  forms  of  the  same  Syllogism. 

All  C  and  some  B  are  equal  to  Y  ; 
All  A  and  all  B  are  equal  to  T  ; 
.-.  Some  C  is  equal  to  all  A  ;  or, 
All  A  is  equal  to  some  C. 

Suppose  that  it  is  known  that  the  fortunes  of  C  and  B  to- 
gether are  larger  than  that  of  Y  (or  all  C  and  some  B  are  equal 


ANALYTIC     OP     SYLLOGISMS.  101 

to  Y),  while  it  has  been  ascertained  that  the  united  fortunes  of 
A  and  B  are  just  equal  that  of  Y  (all  A  and  all  B  are  equal  to 
Y).  We  at  once  infer  that  the  fortune  of  C  is  greater  than  that 
of  A,  for  the  obvious  reason,  that  when  each  is  added  to  the 
same  thing  the  amounts  differ  as  above  stated. 

Again  :  All  C  and  half  or  all  B  are  equal  to  Y  ; 
All  A  and  all  B  are  equal  to  Y  ; 
.-.  All  C  is  equal  to  half  or  all  A. 

So  if  we  should  say  that  C  minus,  multiplied  or  divided  by 
B,  is  equal  to  Y,  and  that  A  similarly  related  to  B  is  equal  to 
Y,  the  conclusion  would  be  A=C.  If  C  thus  related  to  B  is 
equal  Y,  and  A  thus  related  is  greater  or  less  than  Y,  we  have 
the  conclusion  that  C  is  greater  or  less  than  A,  as  the  case 
may  be. 

The  application  of  the  above  examples  to  negative  conclu- 
sions is  so  obvious,  that  little  need  be  said  on  this  topic.  In  all 
instances  in  which  the  relation  of  equality  between  two  concep- 
tions has  been  proven,  that  of  its  absence  and  also  that  of 
greater  or  less  may  be  denied.  So  when  that  of  greater  or  less 
has  been  proved,  the  opposite  of  what  is  proven,  together  with 
the  relation  of  equality,  may  be  denied.     For  example : 

All  C  and  all  B=Y  ; 
All  A  and  all  B  do  not=Y  ; 
.-.  C  and  A  are  not  equal  to  each  other. 

So,  also,  when  two  conceptions  pertain  to  their  objects  as 
always  coexisting,  and  neither  as  existing  separate  from  the 
other,  or  as  sustaining  to  each  other  the  relation  of  universal 
compatibility,  &c,  and  when  the  object  of  a  third  conception  is 
given  as  never  coexisting,  or  as  being  incompatible  with  the 
object  of  either  of  the  others,  the  same  relation  between  this 
third  and  the  remaining  one  may  be  denied.     For  example  : 

C  and  B  always  coexist, — or,  are  universally  compatible  ; 
A  and  B  never  coexist, — or,  are  wholly  incompatible  ; 
.-.  C  and  A  never  coexist, — or,  are  not  compatible. 


General  Remarks  upon  this  form  of  the  Syllogism. 

The  following  general  remarks  upon  this  form  of  the  syllo- 
gism are  deemed  worthy  of  especial  notice  : 

1.  In  it,  the  order  of  the  propositions  is,  to  use  the  language 
of  Sir  William  Hamilton,  "perfectly  arbitrary."  In  other 
words,  the  unfigured  syllogism  has  no  proper  major  and  minor 
terms  or  premises.  A  mere  inspection  of  the  above  examples 
will  render  this  statement  self-evident. 

2.  In  this  syllogism,  also,  the  terms  of  the  conclusion  are  so 
manifestly  and  formally  equivalent  and  definite,  as  far  as  dis- 
tribution is  concerned,  that  conversion  is  almost  if  not  quite 
always  simple,  both  in  thought  and  form.  Each  term  is  given 
as  universal  or  particular. 

3.  This  syllogism  may  also,  with  perfect  propriety,  be  given 
in  the  synthetic  or  analytic  form.  We  may,  for  example,  as 
properly  say,  "  C  and  A  are  equal,"  because  "  A  and  B,  on  the 
one  hand,  and  C  and  B  on  the  other,  are  equal  to  Y,"  as  to 
state  the  premises  first,  and  then  give  the  conclusion  as  an  in- 
ference. 

4.  While  this  form  of  the  syllogism  had,  until  Sir  William 
Hamilton  presented  it,  been  wholly  overlooked  by  logicians,  it 
presents  one  of  the  most  common  and  necessary  forms  of  valid 
reasoning  among  all  classes  of  the  community,  and  especially  in 
the  inductive  sciences.  Without  this  form  of  the  syllogism, 
therefore,  logic,  as  a  science,  would  be  wholly  incomplete  and 
limited  in  its  applications.* 

*  In  justice  to  myself,  and  to  truth,  I  would  say,  that  before  I  had  seen  what  Sir  William 
Hamilton  has  written  upon  this  subject,  or  had  even  heard  that  he  had  spoken  or  written 
any  thing  upon  it,  my  own  independent  investigation  had  led  me  to  a  conception  of  this 
form  of  the  syllogism,  and  to  a  careful  inquiry  into  its  principles  and  laws ;  and  at  the  time 
when  I  read  what  he  has  written,  my  mind  was  employed  in  a  Tain  attempt  to  find  a  place 
for  it,  in  some  department  of  the  figured  syllogism,  and  that  under  the  apprehension,  that 
what  logicians  had  assumed  as  true,  was  so,  to  wit :  that  the  latter  is  the  only  real  form  of 
the  syllogism  itself.  I  saw  clearly,  that  in  many  forms  of  valid  reasoning,  the  terms  com- 
pared did  not  "stand  to  each  other  in  the  reciprocal  relation  of  subject  and  predicate,  being 
in  the  same  proposition,  either  both  subjects,  or  both  predicates.''  I  saw  also,  that  the  ex- 
tremes in  such  case?,  are  not,  as  is  true  of  the  figured  syllogism,  each  singly,  and  by  itself, 
compared  with  the  middle  term;  but,  that  both  alike,  first  one  and  then  the  other,  stand 
with  the  middle,  in  the  common   relation  of  subject  and  predicate ;  and  that,  in  all  such 


ANALYTIC     OF     SYLLOGISMS.  103 

Section  IV. — The  Figured  Syllogism. 

This  form  defined. 

We  now  advance  to  a  special  consideration  of  the  figured  syl- 
logism. That  which  distinguishes  this  form  of  the  syllogism 
from  every  other  is  this,  the  fact  which  we  have  already  stated, 
that  in  all  the  propositions  the  terms  are  related  to  each  other 


Common  assumption  on  the  subject. 

It  has  been  commonly  assumed  that  the  terms  employed  in 
the  various  propositions,  stand  related  to  each  other  as  inferior 
and  superior  conceptions,  the  subject  being  the  inferior  and  the 
predicate  the  superior.  On  this  assumption  the  universal  rules 
of  distribution  are  based,  to  wit :  that  while  all  universal  propo- 
sitions distribute  the  subject,  all  negative  and  no  affirmative 
ones  distribute  the  predicate.  The  latter  principle  can  be  true 
but  upon  the  supposition,  that  the  predicate  is  a  superior  and 
the  subject  an  inferior  conception.  In  the  proposition,  "All 
men  are  mortal,"  for  example,  the  term  mortal  is  not  distributed, 
for  the  reason  that  it  has  a  wider  application  than  the  term  men. 
Suppose  we  say  "X=Z;"  then  the  predicate  as  well  as  the 
subject  is  distributed,  and  that  for  the  obvious  reason  that  Z,  in 
this  proposition,  is  a  conception  in  no  form  or  sense  inferior 
or  superior  to  X.  The  converse  of  the  former  proposition  is, 
"  Some  mortal  beings  are  men,"  while  that  of  the  latter  is 
"Z=X."  In  this  last  judgment  neither  conception  is  inferior 
or  superior  to  the  other,  and,  therefore,  both  terms  are  m  dis- 
tributed. 

cases,  it  made  no  difference  as  to  the  order  of  the  premises.  Yet  I  was  under  the  impres- 
sion, that  after  all,  they  "must  have  a  place  among  the  common  forms  of  the  syllogism,  hav- 
ing no  suspicion  that  there  could  he  any  other  legitimate  form.  From  this  perplexity  I 
was  relieved,  by  the  author  referred  to,  and  shall  ever  esteem  it  a  high  privilege  to  ac- 
knowledge the  obligations  which  I  thereby  owe  to  him. 


Influence  of  Assumptions. 

This  fact  presents  another  example  of  the  influence  of  assump- 
tions. When  they  once  obtain  a  place  in  science  as  first  truths 
or  principles,  the  assumptions  themselves  are  not  examined,  be- 
cause their  truth  is  always  taken  for  granted.  How  true  this  is 
of  the  case  before  us  !  Since  the  days  of  Aristotle  the  principle 
has  been  assumed,  that  in  all  propositions,  with  accidental  ex- 
ceptions, the  subject  is  the  inferior  and  the  predicate  the  supe- 
rior conception  ;  and  from  hence,  the  principle  that  no  affirma- 
tive proposition  distributes  the  predicate.  "It  may  happen, 
indeed,"  says  Dr.  Whately,  "  that  the  whole  of  the  predicate  in 
an  affirmative  may  agree  with  the  subject ;  e.  g.  it  is  equally 
true,  that  'All  men  are  rational  animals,'  and  'All  rational 
animals  are  men  ;'  but  this  is  merely  accidental,  and  is  not  at 
all  implied  in  the  form  of  expression,  which  alone  is  regarded 
in  logic." 

It  is  true,  as  Dr.  Whately  observes,  that  in  cases  where  the 
whole  predicate  in  an  affirmative  proposition  agrees  with  the 
whole  subject,  the  fact  does  not  appear  from  the  mere  form  of 
expression ;  and  it  is  equally  true,  on  the  other  hand,  that 
from  the  mere  form  of  the  expression  it  does  not  appear  when 
the  whole  predicate  does  not  agree  with  the  whole  subject. 
This  fact  is  always  to  be  determined  by  the  nature  of  the  con- 
ceptions compared,  and  the  nature  of  the  relations  between 
them. 

Principles  determining  the  distribution  of  the  Predicate. 

We  are  now  prepared  for  a  distinct  statement  of  the  princi- 
plesVhich  determine  the  distribution  and  non-distribution,  not 
only  of  the  subject,  but  predicate  in  all  judgments  employed  in 
reasoning.     They  are  the  following  : 

1.  Whenever  the  subject  and  predicate  stand  related  as  infe- 
rior and  superior  conceptions,  then  they  follow  the  rules  of  dis- 
tribution commonly  laid  down  in  treatises  on  logic,  to  wit : 
(1.)  All  universal   propositions  (and   no»  particular)   distribute 


ANALYTIC     OF     SYLLOGISMS.  105 

the  subject :  (2.)  All  negative  (and  no  affirmative)  the  predi- 
cate. 

2.  Whenever  the  terms  of  a  proposition  belong  to  the  same 
class,  and  are  compared  relatively  to  the  principle  of  equality 
and  difference,  as  equal,  greater,  or  less,  or  when  they  fall  under 
the  relation  of  proximity  or  distance  in  time,  or  place,  &c,  then 
in  affirmative  and  negative  propositions  alike,  the  predicate  fol- 
lows the  same  principles  of  distribution  as  the  subject.  So, 
when  the  subject  and  predicate  are  correlative  terms ;  as, 
"  Father  and  son  ;  cause  and  effect,"  &c,  neither,  as  a  con- 
ception, is  superior  to  the  other ;  and  the  predicate,  when  it 
as  the  correlative  of  the  subject  becomes  by  conversion  the 
subject,  its  quantity  is  the  same  as  that  of  the  subject  was. 
Finally,  when  the  predicate  is  used  to  define  the  subject,  the 
same  principle  obtains.  The  proposition,  for  example,  "  A-  is 
the  cause  of  B,"  when  converted  becomes,  "  B  is  the  effect 
of  A." 

That  the  rules  of  distribution  above  stated  are  applicable  uni- 
versally to  all  propositions  of  the  first  class,  is  too  evident  to  re- 
quire much  elucidation.  In  all  cases  where  any  class  of  facts 
are  placed  under  a  universal  principle,  as,  for  example,  "  Murder 
is  criminal,"  "  Such  and  such  actions  are  right  or  wrong  ;"  or, 
when  any  individual  conception  is  ranked  under  a  specifical,  or 
one  or  the  other  of  these  under  a  generical  conception,  as  in  the 
judgments,  "  John  is  a  man,"  "  All  men  are  mortal,"  &c. ;  in  all 
such  cases  the  predicate  has  a  wider  application  than  the  sub- 
ject, and  is  hence  never  distributed  in  affirmative  propositions. 
Even  in  negative  propositions,  the  term  which  has  in  itself  the 
wider  application  is  most  commonly,  though  not  always,  the 
predicate.  Thus,  in  the  language  of  another,  it  is  more  natural 
to  say,  that  " The  apostles  were  no  deceivers,"  than  that  "  No 
deceivers  are  apostles." 

Let  us  now  look  at  propositions  of  the  second  class  of  judg- 
ments. When  we  say"X=Z,"for  example,  the  two  terms 
are  compared  throughout  their  whole  extent,  and  if  one  is 
distributed,  the  other  of  course  must  be,  or  the  equality 
would  not  exist.  Conversion,  in  all  such  cases,  is  simple,  and 
5' 


106  LOGIC, 

never  by  limitation.  If  we  say  "  X  is  greater  than  Z,"  the 
converse  holds  universally,  "Z  is  less  than  X;"  each  term 
being  alike  and  equally  distributed  in  both  cases.  If  we  say, 
"  X  is  the  cause  of  Z,"  then  in  the  converse,  Z  is  given  equal- 
ly universally,  in  the  correlative  form,  as  the  effect  of  X.  The 
distribution  of  the  subject  and  the  predicate  in  both  cases  is 
equal. 

The  same  may  be  shown  to  hold  true  in  all  the  cases  which 
are  given  as  falling  under  this  class.  From  the  nature  of  the 
case  it  cannot  be  otherwise.  We  are  not  here  endeavoring  to 
find  under  what  superior  conception  a  given  inferior  one  ranks, 
or  what  inferior  conception  any  given  superior  one  includes. 
We  are  not  inquiring  under  what  general  principle  any  given 
class  of  facts  are  to  be  classed.  But  we  are  inquiring  in  regard 
to  objects  of  the  same  class,  and  that  relatively  to  the  question 
of  their  agreement  or  disagreement ;  as,  whether  they  are  equal 
or  unequal,  which  is  the  greater  and  which  the  less,  &c.  In  all 
such  cases  it  makes  no  difference  whatever  which  term  is  the 
subject  and  which  the  predicate  ;  both,  in  all  cases,  being  equal- 
ly distributed. 

Fundamental  mistake  in  developing  the  science  of  Logic. 

In  all  treatises  on  the  science  of  logic,  as  far  as  we  know,  with 
the  exception  of  Sir  William  Hamilton's  works,  and  "  Thomp- 
son's Laws  of  Thought,"  the  figured  syllogism  has  been  consid- 
ered as  covering  all  forms  of  the  categorical  argument.  In  de- 
veloping the  syllogism  it  has  also  been  assumed,  as  we  have 
said,  that  the  terms  employed  in  the  syllogism  are  related  as  in- 
ferior and  superior  conceptions.  Now  while  the  science  of  logic 
is  developed  upon  such  principles,  it  must  remain  as  one  of  the 
most  imperfect  and  unsatisfactory  of  all  the  sciences.  Take  the 
principle  laid  down  as  holding  universally,  that  no  affirmative 
propositions  distribute  the  predicate,  and  apply  it  to  any  of  the 
processes  in  the  mathematics,  and  we  shall  find  it  wholly  to  fail ; 
for  these  almost,  if  not  quite  universally,  distribute  the  predicate 
equally  with  the  subject.     The  entire  science  of  the  mathematics 


ANALYTIC     0E     SYLLOGISMS.  107 

is  based  upon  illogical  principles,  if  this  principle  is  correct. 
Every  one  of  its  principles  is  convertible,  not  by  limitation, 
but  simply.  So  of  its  subsequent  deductions,  not  one  of  them 
accord  with  the  principle,  that  no  affirmative  propositions  dis- 
tribute the  predicate.  Take,  as  an  example,  the  proposition, 
"  The  square  of  the  hypothenuse  of  a  right-angled  triangle  is 
equal  to  the  sum  of  the  squares  of  its  two  sides."  If  no  affirm- 
ative propositions  distribute  the  predicate,  and  the  universal 
affirmative  ones  can  be  conveited  but  by  limitation,  then  the 
converse  of  the  above  proposition  would  be  this  :  "  Some  part 
of  the  sum  of  the  squares  of  the  two  sides  of  such  triangle 
equals  the  square  of  the  hypothenuse."  But  this  is  not  the  con- 
verse of  the  above  proposition ;  that  converse  being  universal 
and  not  particular,  and  that  for  the  reason  that  all  universal 
affirmative  propositions  of  this  class  distribute  the  predicate  as 
well  as  the  subject.  Nor  are  such  propositions  of  unfrequent 
occurrence.  We  everywhere  meet  them  in  almost  all  depart- 
ments of  human  thought,  Indeed,  it  may  be  questioned  which 
is  most  numerous,  those  universal  affirmative  propositions  which 
do,  and  those  which  do  not,  distribute  the  predicate  as  well  as 
the  subject,  Take  another  example  from  common  life,  to  wit : 
"  A  resembles  or  is  unlike  B."  The  converse  of  all  such  propo- 
sitions is  not  a  particular  but  a  universal  affirmative,  to  wit : 
"  B  resembles  or  is  unlike  A."  We  need  not  add  further  illus- 
trations. 

DIVISION    OF   THE   PRESENT   SUBJECT.  , 

In  further  elucidating  the  figured  syllogism,  we  propose  to 
pursue  the  following  order  of  investigation  : 

1.  Those  forms  of  the  syllogism  which  have  been  commonly 
treated  of  as  including  all  forms  of  the  categorical  argument,  to 
wit :  those  forms  in  which  the  terms  employed  are  related  to 
each  other  as  inferior  and  superior  conceptions. 

2.  Those  forms  in  which  affirmative  propositions  as  well  as 
negative  distribute  the  predicate. 

3.  We  shall  then  combine  the  two  classes,  and  endeavor  to 
develop  the  general  laws  of  the  figured  syllogism  as  such. 


I.  Those  forms  of  the  syllogism  which  have  been  com- 

NONLY  TREATED  OF  AS  INCLUDING  ALL  FORMS  OF  THE  CATE- 
GORICAL ARGUMENT,  TO  WIT  :  THOSE  FORMS  IN  WHICH  THE 
TERMS  EMPLOYED  ARE  RELATED  TO  EACH  OTHER  AS  INFERIOR 
AND    SUPERIOR   CONCEPTIONS. 

In  entering  upon  the  investigations  which  follow,  we  would 
request  the  reader  to  keep  distinctly  in  mind  the  kind  of  judg- 
ments to  he  treated  of,  to  wit :  those  in  which  the  subject  and 
predicate  represent  respectively  inferior  and  superior  concep- 
tions ;  conceptions  related  to  each,  as  individual,  specifical,  and 
generical  conceptions. 


PRELIMINARY     REMARKS     UPON     THIS     FORM     OF     THE    FIGURED 
SYLLOGISM. 

Before  we  proceed  further,  we  would  invite  special  attention 
to  the  following  preliminary  remarks  upon  the  department  of 
the  subject  before  us. 

Only  proximate  conclusions  obtained. 

On  a  moment's  reflection  it  will  appear  perfectly  evident, 
that  in  this  form  of  the  syllogism  we  obtain  only  conclusions 
approximating  the  truth  ;  that  is,  we  determine  not  what  indi- 
viduals are  in  themselves,  but  with  what  class  or  classes  they 
take  rank.    Take,  for  example,  the  following  syllogism : 

All  men  are  mortal ; 
C  is  a  man  ; 
.*.  C  is  mortal,  i.  e.  some  mortal  being. 

We  have  here  determined  not  the  special  characteristics  of 
C,  but  the  particular  and  special  class  to  which  he  belongs. 
This  is  the  character  of  all  conclusions  obtained  through  this 
form  of  the  syllogism,  and  from  the  nature  of  the  case  it  must 
be  so. 


ANALYTIC     OF     SYLLOGISMS.  109 

The  principle  of  Extension  and  Intension,  or  of  Breadth  and 
Depth,  as  applied  to  the  Syllogism. 

In  our  elucidation  of  superior  and  inferior  conceptions  we 
showed  that,  while  the  matter  of  the  latter  is  much  greater  than 
that  of  the  former,  the  sphere  of  the  former  is  in  a  correspond- 
ing degree  more  extensive  than  that  of  the  latter.  In  regard 
to  matter,  the  individual  conception  embraces  more  elements 
than  the  specifical,  and  this  last  more  than  the  generical.  At 
the  same  time,  this  last  conception  is  applicable  to  more  objects 
than  the  second,  and  the  second  to  more  than  the  first.  The 
terms  extension  and  intension,  breadth  and  depth,  are  em- 
ployed by  Sir  William  Hamilton  to  represent  these  two  oppo- 
site principles.  In  regard  to  depth  (the  matter  of  the  concep- 
tion), the  individual  is  the  lowest  of  all ;  that  is,  includes  the 
greatest  number  of  elements.  In  regard  to  breadth,  the  num- 
ber of  objects  which  the  conception  represents,  that  is,  rela- 
tively to  its  sphere,  the  generical  conception  is  the  most  exten- 
sive of  all  others.  The  two  quantities  are  in  relations  perfectly 
reverse  to  each  other.  The  greater  the  depth,  the  less  the 
breadth  of  a  conception  ;  and  the  greater  its  breadth,  the  less  its 
depth.  In  regard  to  breadth,  the  inferior  conception  is  con- 
tained under  the  superior.  In  regard  to  depth,  the  superior  is 
contained  in  the  inferior. 

In  this  form  of  the  figured  syllogism  the  propositions  always 
refer  to  one  or  the  other  of  these  principles.  In  affirmative 
propositions  the  subject  is  an  inferior  conception,  and  the  predi- 
cate a  superior.  When  of  the  two  conceptions  in  a  negative 
proposition  one  has  the  greater  breadth  than  the  other,  this 
one,  as  we  have  before  said,  is  commonly  the  predicate. 

Now  every  proposition  whose  subject  is  an  inferior  and  pred- 
icate a  superior  conception,  may  be  understood  relatively  to  the 
principle  of  intension  (depth)  or  extension  (breadth),  and  the 
meaning  of  the  proposition  will  be  as  the  principle  to  which  it 
is  referred.  Thus  the  proposition,  "All  men  are  mortal," 
means,  in  regard  to  intension,  that  the  quality  represented  by 
the  term  mortal,  or  mortality,  belongs  to  every  individual  of 


the  race ;  and  in  regard  to  extension,  that,  all  men  belong  to 
the  class  of  mortal  beings. 

In  further  elucidation  of  this  very  important  department 
of  our  subject,  we  "here  present  the  following  extract  from 
"Thomson's  Laws  of  Thought."  Of  the  last  two  examples 
cited  at  the  close  of  the  extract,  we  would  remark  that  the 
term  TJ  designates  toto-total  affirmative  propositions — those  in 
which  both  subject  and  predicate  are  distributed  ;  and  Y  parti- 
total  affirmatives — those  in  which  the  subject  is  particular  and 
the  predicate  universal ;  as,  "  Some  X  is  all  of  Z." 

"Import  of  Judgments  {Extension  and  Intension — Naming). 

"  Upon  the  examination  of  any  judgment  which  appears  to 
express  a  simple  relation  between  two  terms,  we  shall  find  it 
really  complex,  and  capable  of  more  than  one  interpretation. 
'  All  stones  are  hard,'  means,  in  the  first  place,  that  the  mark 
hardness  is  found  among  the  marks  or  attributes  of  all  stones ; 
and  in  this  sense  of  the  judgment  the  predicate  may  be  said  to 
be  contained  in  the  subject,  for  a  complete  notion  of  stones  con- 
tains the  notion  of  hardness  and  something  more.  This  is  to 
read  the  judgment  as  to  the  intention  (or  comprehension)  of  its 
terms.  Where  it  is  a  mere  judgment  of  exj:>lanation,  it  will 
mean,  '  the  marks  of  the  predicate  are  among  what  I  know  to 
be  among  the  marks  of  the  subject ;'  but  where  it  is  the  expres- 
sion of  a  new  step  in  our  investigation  of  an  accession  of  know- 
ledge, it  must  mean,  '  the  marks  of  the  predicate  are  among 
what  I  now  find  to  be  the  marks  of  the  subject.' 

"  Both  subject  and  predicate,  however,  not  only  imply  cer- 
tain marks,  but  represent  certain  sets  of  objects.  When  we 
think  of  '  all  stones,'  we  bring  before  us  not  only  the  set  of 
marks — as  hardness,  solidity,  inorganic  structure,  and  certain 
general  forms — by  which  we  know  a  thing  to  be  what  we  call 
a  stone,  but  also  the  class  of  things  which  have  the  marks,  the 
stones  themselves.  And  we  might  interpret  the  judgment, 
'  All  stones  are  hard,'  to  mean  that,  '  The  class  of  stones  is  con- 
tamed  in  the  class  of  hard  things.'     This  brings  in  only  the  ex- 


ANALYTIC     OF     SYLLOGISMS.  Ill 

tension  of  the  two  terms  according  to  which,  in  the  example 
before  us,  the  subject  is  said  to  be  contained  in  the  predicate. 
Every  judgment  may  be  interpreted  from  either  point  of  view  ; 
and  a  right  understanding  of  this  doctrine  is  of  great  impor- 
tance. Let  it  be  noticed,  against  a  mistake  which  has  been  re- 
introduced into  logic,  that  all  conceptions,  being  general,  repre- 
sent a  class  ;  and  that  to  speak  of  a  '  general  name'  which  is  not 
the  name  of  a  class  is  a  contradiction  of  terms.  But  this  is  very 
different  from  asserting  that  a  class  of  things  corresponding . 
to  the  conception  actually  exists  in  the  world  without  us.  The 
conceptions  of '  giants,'  '  centaur,'  and  '  siren,'  are  all  of  classes  ; 
but  every  one  knows  who  realizes  them,  that  the  only  region  in 
which  the  classes  really  exist,  is  that  of  poetry  and  fiction.  The 
mode  of  existence  of  the  things  which  a  conception  denotes  is  a 
mark  of  the  conception  itself;  and  would  be  expressed  in  any 
adequate  definition  of  it.  It  would  be  insufficient  to  define 
'  centaurs'  as  a  set  of  monsters,  half  men  and  half  horses,  who 
fought  with  the  Lapithae,  so  long  as  we  left  it  doubtful  whether 
they  actually  lived  and  fought,  or  only  were  feigned  to  have 
done  so  ;  and  by  some  phrase,  such  as  '  according  to  Ovid,'  or, 
'in  the  mythology,'  we  should  probably  express  that  their 
actual  existence  was  not  part  of  our  conception  of  them. 

"  The  judgment  selected  as  our  example  contains  yet  a  third 
statement.  We  observe  marks  ;  by  them  we  set  apart  a  class  ; 
and,  lastly,  we  give  a  class  or  name  a  symbol  to  save  the  trou- 
ble of  reviewing  all  the  marks  every  time  we  would  recall  the 
conception.  '  All  stones  are  hard,'  means  that  the  name  hard 
may  be  given  to  every  thing  to  which  we  apply  the  name 
stones. 

"All  judgments,  then,  may  be  interpreted  according  to  their 
intension,  their  extension,  and  their  application  of  names  or  de- 
scriptions ;  as  the  following  examples  may  help  to  show  : 

"A.    '  All  the  metals  are  conductors  of  electricity,'  means  : 

"Intension. — The  attribute  of  conducting  electricity  belongs  to  all 

metals. 
"Extension. — The  metals  are  in  the  class  of  conductors  of  electricity. 
•'  Nomenclature. — The  name  of  conductors  of  electricity  may  be  ap- 
plied to  the  metals  (among  other  things). 


112  LOGIC. 

"  E.   '  None  of  the  planets  move  in  a  circle,'  means  : 

"Internum. — The  attribute  of  moving  in  a  circle  does  not  belong  to 
any  planet. 

"Extension. — None  of  the  planets  are  in  the  class  (be  it  real,  or  only 
conceivable)  of  things  that  move  in  a  circle. 

"  Nomenclature. — The  description  of  things  that  move  in  a  circle  can- 
not be  applied  to  the  planets. 
"I.    ' Some  metals  are  highly  ductile,'  means  : 

"  Intension. — The  mark  of  great  ductility  is  a  mark  of  some  metals. 

"Extension. — Some  metals  are  in  the  class  of  highly  ductile  things. 

"Nomenclature. — The  name  of  highly  ductile  things  may  be  applied 
tosome  metals. 
"  0.   '  Some  lawful  actions  are  not  expedient,'  means  : 

"  Intension. — The  attribute  of  expediency  does  not  belong  to  some 
lawful  actions. 

' :  Extension.—  Some  lawful  actions  do  not  come  into  the  class  of  expe- 
dient things. 

"Nomenclature.- — The  name  of  expedient  cannot  be  given  to  some 
lawful  actions. 
"  U.   '  Rhetoric  is  the  art  of  persuasive  speaking,'  means  : 

"Intension. — The  attributes  of  the  art  of  persuasive  speaking,  and  of 
rhetoric,  are  the  same. 

"Extension. — Rhetoric  is  coextensive  with  the  art  of  speaking  per- 
suasively. 

"Nomenclature. — 'The  art  of  persuasive  speaking'  is  an  expression 
which  may  be  substituted  for  rhetoric. 
"  T.  '  The  class  of  animals  includes  the  polyps,'  means  : 

"  Intension. — The  attributes  of  all  the  polyps  belong  to  some  animals. 

"  Extension. — The  polyps  are  in  the  class  of  animals. 

"  Nomenclature. — The  name  of  polyps  belongs  to  some  animals." 

Direct  and  indirect  conclusion. 

All  are  aware  that  in  every  valid  syllogism  there  are  two 
conclusions  deducible  from  the  premises  laid  down.  One  of 
these  conclusions  is  direct  and  immediate,  and  the  other  often, 
though  not  always,  as  we  shall  see,  indirect.  In  the  premises, 
for  example,  "  All  M  is  X,  and  all  Z  is  M,"  we  have  the  direct 
conclusion,  that  "  All  Z  is  X."  The  converse  of  this  is,  "  Some 
X  is  Z,"  and  this  last  proposition  may  be  called  the  indirect 
conclusion.  It  is  optional,  in  view  of  the  premises,  to  draw  first 
the  direct  conclusion,  and  then  by  conversion  to  obtain  the  in- 


dire' 


ANALYTIC     OF     SYLLOGISMS. 


rect  conclusion,  or  to  assume  this  last  inference  as  implied  in 
the  premises. 

Character  of  all  the  propositions  employed  in  this  form  of  the 
Syllogism. 

The  character  of  all  the  propositions  of  this  form  of  the  syllo- 
gism next  claims  our  attention.  Every  premise  and  conclusion 
is  either  a  universal  affirmative  proposition  (A),  a  proposition 
with  a  distributed  subject  and  an  undistributed  predicate ;  a 
particular  affirmative  (I)  with  both  the  subject  and  predicate 
undistributed ;  a  universal  negative  with  both  terms  distribu- 
ted (E) ;  or,  finally,  a  particular  negative  with  the  subject  undis- 
tributed and  the  predicate  distributed  (O).  All  propositions  con- 
stituted of  inferior  and  superior  conceptions  must  belong  to  one 
or  the  other  of  these  classes. 

Letters  to  be  employed. 

In  further  prosecuting  our  investigations  we  will,  in  elucida- 
ting the  syllogism,  make  use  of  the  letters  X  and  Z  to  represent 
the  extremes,  and  M  to  represent  the  middle  term. 


CANON  AND  LAWS  OF  THIS  FORM  OF  THE  SYLLOGISM CONDI- 
TIONS O?  WHICH  WE  CAN  OBTAIN  THE  DIFFERENT  CLASSES 
OF    CONCLUSIONS    ABOVE   NAMED;    THAT   IS,    A,    I,    E,    O. 

We  now  advance  to  a  very  important  inquiry,  to  wit :  the 
special  relations  of  the  extremes  to  the  middle  term,  relations  in 
which  we  can  obtain  these  different  classes  of  conclusions. 


Universal  Affirmative  Conclusions. 

There  is  but  one  conceivable  relation  of  two  such  terms  to  a 
common  third  term,  a  relation  from  which  a  universal  affirm- 
ative conclusion  can  be  deduced,  to  wit :  when  all  of  the  mid- 
dle is  contained  hi  one  extreme,  and  all  of  the  other  extreme  is 


114  LOGIC. 

itself  contained  in  said  term.  If  all  of  M  is  in  X  and  all  of  Z  is 
M,  then,  of  course,  all  of  Z  must  be  in  X.  Change  the  relations 
of  the  terms  in  any  form  or  degree,  and  it  will  at  once  be  per- 
ceived that  no  such  conclusion  can  then  be  logically  deduced. 
Stated  in  form  this  is  the  relation  referred  to  : 

All  M  is  X  ; 
All  Z  is  M  ; 
.-.  AllZisX. 


Universal  Negative  Conclusions. 

There  are  two  relations  of  the  extremes  to  the  middle  term 
from  which  universal  negative  conclusions  arise,  namely : 

1.  That  in  which  all  of  the  middle  term  is  excluded  from  one 
extreme,  and  all  of  the  other  is  included  in  said  term.  If  none 
of  M  is  in  X,  and  all  of  Z  is  in  M,  then,  of  course,  none  of  Z  is 
in  X.    From  this  relation  we  have  one  form  of  argument ; 

No  M  is  X  ; 
All  Z  is  M  ; 
.-.  NoZisX. 

2.  When  all  of  one  extreme  is  included  in  the  middle  term, 
and  all  of  the  other  is  excluded  from  said  term.  If,  for  exam- 
ple, all  of  X  is  in  M  and  none  of  Z  is  in  M,  of  necessity,  none  of 
Z  is  in  X.     Here  we  have  two  forms,  to  wit : 

No  X  is  M  ;  All  X  is  M  ; 

All  Z  is  M  ;  No  Z  is  M  ; 

.-.  NoZisX.  .-.  NoZisX. 


Particular  Affirmative  Conclusions. 

There  are  three  relations  of  two  terms  to  a  common  third 
term,  relations  from  which  particular  affirmative  conclusions 
may  be  logically  deduced.     They  are  the  following : 

1.  When  all  of  the  middle  term  is  contained  in  one  extreme, 
and  part  of  the  other  extreme  is  contained  in  said  term.  So 
far  as  this  part,  which  is  common  to  the  two  extremes,  is  con- 


ANALYTIC      OF     SYLLOGISMS.  115 


cerned,  they  must  agree  with  each  other,  and  a  particular  affirm- 
ative conclusion  is  logically  valid.  If  all  of  M  is  in  X  and  a 
part  of  Z  is  in  M,  then,  of  course,  a  part  at  least  of  Z  must  be 
in  X  ;  and  the  proposition,  "  Some  Z  is  X,"  will  be  valid.  Of 
this  class  Ave  have  one  example,  to  wit : 

All  M  is  X  ; 
Some  Z  is  M  ; 
.-.  Some  Z  is  X. 

2.  When  all  of  the  middle  term  is  contained  in  each  extreme. 
If  all  of  M  is  in  both  X  and  Z,  then,  so  far  as  each  contains  M, 
they  must  agree,  and  the  proposition,  "  Some  Z  is  X,"  must  be 
logically  valid.     Of  this  class,  also,  we  have  but  one  example : 

All  M  is  X  ; 

All  M  is  Z  ; 

.•.  Some  Z  is  X. 

3.  When  all  of  the  middle  term  is  contained  in  one  extreme 
and  part  of  it  in  the  other.  So  far  as  this  part,  which  is  com- 
mon to  the  two  extremes,  is  concerned,  they  must  agree  with 
each  other,  and  the  conclusion,  "  Some  Z  is  X,"  must  be  held  as 
logically  valid.  Under  this  division  we  have  two  forms  of  valid 
argument.     For  example : 

All  M  is  X  ;  Some  M  is  X  ; 

Some  M  is  Z  ;  All  M  is  Z  ; 

.-.  Some  Z  is  X.  .-.  Some  Z  is  X, 


JParticular  Negative  Conclusions. 

In  the  following  relations  particular  negative  conclusions  are 
valid. 

1.  When  some  of  one  extreme  is  contained  in  the  middle 
term  and  the  whole  of  the  other  is  excluded  from  it.  In  this 
case  the  part  of  the  one  extreme  contained  in  the  middle  must 
be  excluded  from  the  other  extreme,  all  of  which  is  excluded 
from  the  middle  term,  and  the  conclusion,  "  Some  Z  is  not  X," 
is  valid.  We  would  here  remark  that  a  part  of  one  term  is 
contained  in  another,  when  the  former  in  the  same  proposition 


116  LOGIC. 

as  the  latter  is  the  subject  of  a  particular,  or  the  predicate  of  a 
universal  or  particular  affirmative  proposition.  A  part  of  X, 
for  example,  is  equally  contained  in  M  in  the  propositions, 
"  Some  X  is  M,"  "  All  M  is  X,"  and  "  Some  M  is  X."  In  this 
relation  we  have  the  following  forms : 

(1.)  (2.)  (3.) 

■    NoMisX;  No  X  is  M  ;  No  M  is  X. 

Some  Z  is  M  ;  '  Some  Z  is  M  ;  All  M  is  Z  ; 

.  •.  Some  Z  is  not  X.  .  ■.  Some  Z  is  not  X.  .  \  Some  Z  is  not  X. 

(4.)  (5.)  .        (6.) 

No  M  is  X  ;  No  X  is  M  ;  No  X  is  M  ; 

Some  M  is  Z  ;  All  M  is  Z  :  Some  M  is  Z  ; 

.  \  Some  Z  is  not  X.  .  •.  Some  Z  is  not  X.  .  \  Some  Z  is  not  X. 

2.  When  the  whole  of  one  extreme  is  contained  in  the  mid- 
dle and  a  part  of  the  other  excluded  from  it.  In  this  case  the 
part  excluded  from  the  middle  must,  of  course,  be  excluded 
from  the  other  extreme,  all  of  which  is  included  in  the  middle 
term.     Of  this  form  we  have  one  example  : 

All  X  is  M  ; 
Some  Z  is  not  M  ; 
.-.  Some  Z  is  not  X. 

3.  When  a  part  of  the  middle  term  is  excluded  from  one  ex- 
treme and  all  of  it  contained  in  the  other.  In  this  relation, 
also,  but  one  single  form  presents  itself,  to  wit : 

Some  M  is  not  X  ; 
All  M  is  Z  ; 
.-.  Some  Z  is  not  X. 


All  valid  conclusions  deduced  upon  principles  which  accord 
with  those  above  elucidated. 

From  a  careful  examination  of  the  above  statements  and  ex- 
amples, it  will  be  seen  not  only  that  when  the  above  relations 
do  exist  between  the  extremes  and  the  middle  term,  the  dif- 
ferent forms  of  conclusions  referred  to  do  arise,  but  that  to  de- 
duce any  legitimate  conclusions  of  any  kind,  relatively  to  infe- 


ANALYTIC     OF     SYLLOGISMS.  117 

rior  and  superior  conceptions  related  to  each  other  as  subject 
and  predicate,  these  relations  must  exist.  From  no  conceivable 
relations  of  X  and  Z  to  M,  for  example,  can  we  affirm  that 
"Every  Z  is  X,"  but  this,  that  "All  of  M  is  X  and  all  of  Z 
is  M."  Vary  these  relations  in  any  form  or  degree  whatever, 
and  it  will  be  seen  at  once  that  from  such  relations  no  such  con- 
clusion can  be  deduced.  The  same  holds  true  in  all  the  other 
cases  named.  Let  us  now  analyze  these  relations  for  the  pur- 
pose of  deducing  from  them  the  general  laws  of  the  figured  syl- 
logism, especially  in  the  form  we  are  now  considering  it.* 


Analysis  of  the  above  relations. 

1.  The  fact  which  Ave  first  notice  is  this,  that  in  all  these  forms 
of  argument  we  have,  at  last,  one  affirmative  premise.  In  all 
logically  valid  arguments,  then,  one  premise  at  least  must  be 
affirmative  ;  in  other  words,  from  exclusively  negative  premises 
no  relations  between  the  extremes  can  be  affirmed  or  denied. 
From  the  fact  that  two  terms  disagree  with  a  common  third 
term,  we  cannot  affirm  that  they  agree  or  disagree  with  each 
other,  for  the  reason  that  while  they  both  do  thus  disagree  with 
this  term,  they  may  either  agree  or  disagree  with  each  other. 
A  and  B  may  differ  in  size  and  weight  from  C,  and  one  be 
equal  or  unequal  in  all  particulars  to  the  other. 

2.  We  notice,  also,  the  fact  that  when  the  conclusion  is 
affirmative  both  premises  are  affirmative,  and  that  when  we 
have  a  negative  conclusion  one  of  the  premises  is  negative. 
From  the  nature  of  the  relations  of  the  extremes  to  the  middle 
term  this  must  be  the  case.  When  the  relation  of  the  extremes 
to  the  middle  term  is  positive,  that  is,  when  both  agree  with 
that  term,  their  relations  to  each  other  must  be  positive  also. 
When  you  affirm  of  the  relation  of  one  extreme  to  the  middle 
term  what  you  deny  of  the  other,  a  corresponding  disagree- 

*  With  very  few  if  any  exceptions  these  principles  apply  to  all  forms  of  the  syllogism, 
especially  to  the  figured  one.  As  thus  applicable  these  principles  should  be  studied,  as  they 
present  the  only  relations  between  the  extremes  and  the  middle  term  which  authorize  in- 
ferences of  any  kind. 


118  LOGIC. 

ment  must  be,  of  course,  affirmed  of  the  extremes  themselves. 
Hence  the  general  principle  that  when  both  premises  are  affirm- 
ative the  conclusion  must  be  affirmative,  and  when  one  premise 
is  negative  such  must  be  the  character  of  the  conclusion. 

3.  We  notice,  further,  that  in  all  cases  one  of  the  premises  is 
universal.  From  the  fact  that  of  the  two  extremes  each  partly 
agrees,  or  that  one  in  part  agrees,  and  the  other  similar]}'  disa- 
grees with  the  middle  term,  we  can  'draw  no  legitimate  infer- 
ence in  regard  to  their  agreement  or  disagreement  with  each 
other ;  because  the  points  of  agreement  or  disagreement  may 
not  be  the  same  at  all,  and  the  extremes,  therefore,  may  not  be 
compared  with  the  same  thing.  Suppose,  for  illustration,  that 
M  has  three,  and  only  three,  kinds  of  currency  in  his  possession, 
to.  wit,  gold,  silver,  and  paper ;  while  X  has  the  first  kind  and  Z 
the  second.  Each,  in  what  he  possesses,  agrees  in  some  respects 
with  M,  yet  neither  agrees  with  the  other.  From  the  fact,  then, 
that  two  terms  mutually  agree  or  disagree  in  some  respects 
with  a  third,  we  cannot  legitimately  affirm  or  deny  any  form  of 
agreement  or  disagreement  between  those  terms  themselves. 
Suppose,  further,  that  X  has  gold  coin  and  Z  copper ;  so  far, 
then,  the  former  agrees  and  the  latter  disagrees  with  M.  From 
this  fact,  however,  we  cannot  legitimately  infer  that  Z  has  some- 
thing (copper  coin)  which  X  has  not ;  for  the  latter,  from  aught 
that  appears  in  the  premises,  may  have  copper  as  well  as  gold 
coin,  and  thus  agree  with  Z  as  well  as  M.  In  all  legitimate 
forms  of  argument,  therefore,  one  premise  at  least  must  be 
universal.  In  other  words,  from  particular  premises  we  can 
infer  nothing. 

4.  From  a  careful  examination  of  the  above  relations  it  will 
also  be  seen,  that  in  every  case  the  middle  term  is  given  as  the 
subject  of  a  universal,  or  the  predicate  of  a  negative  proposition. 
In  all  legitimate  forms  of  argument  this  condition  is,  and  must 
be,  fulfilled.  From  the  fact  that  all  X  and  all  Z  are  in  M,  we 
cannot  logically  conclude  that  any  part  of  Z  is  in  X ;  for  Z, 
from  any  thing  presented  in  the  premises,  may  be  in  one  part  of 
M  and  X  in  another,  and  neither  have  any  form* of  agreement 
or  disagreement  with  the  same  thing.     So  from  the  fact  that 


ANALYTIC     OF     SYLLOGISMS.  119 

all  X  is  in  M  and  some  of  M  is  not  in  Z,  we  cannot  legitimately 
affirm  that  some  part  of  Z  is  not  in  X  ;  for  all  of  Z  may,  notwith- 
standing what  is  affirmed  in  the  premises,  be  in  the  part  of  M  in 
which  X  is.  In  all  forms  of  argument,  logically  correct  forms,' 
which  we  are  now  speaking  of,  and  which  are  included  in  the 
sphere  of  the  figured  syllogism,  the  middle  term  must  he  the 
subject  of  a  universal  or  the  predicate  of  a  negative  proposition  ; 
that  is,  must  be  distributed,  at  least,  once  in  the  premises.  Nor 
is  it  needful,  as  will  appear  from  an  analysis  of  the  above  cases, 
that  it  be  distributed  more  than  once ;  for  if  the  whole  of  this 
term  is  compared,  as  it  is  in  the  relations  supposed,  with  one  ex- 
treme and  a  part  only  of  it  with  the  other,  so  far  they  must  be 
compared  with  the  same  thing,  and  so  far,  therefore,  their  rela- 
tions to  each  other  may  from  hence  be  determined. 

5.  In  all  the  cases  before  us,  we  remark  again,  that  the  terms 
of  the  conclusion  are  definite  or  indefinite ;  that  is,  distributed 
or  not  distributed  just  as  they  were  in  the  premises.  This  is  a 
universal  law  of  the  figured  syllogism,  and  hence  the  rule :  no 
term  must  be  distributed  in  the  conclusion  which  was  not  dis- 
tributed in  the  premises.  Where  this  rule  is  violated  (the  vio- 
lation being  called  an  illicit  process  of  the  term  thus  employed), 
something  is  affirmed  universally  in  the  conclusion  which  was 
only  affirmed  partially  in  the  premises. 

Note. — It  is  not  necessary  that  every  term  which  was  dis- 
tributed in  the  premises  should  be  distributed  in  the  conclusion, 
though  such  a  use  may  always  be  made  of  it ;  but  when  a  uni- 
versal conclusion  is  valid,  the  particular  which  comes  under  it  is 
valid  also. 

TJie  Canon  of  this  Syllogism. 

"We  are  now  prepared  to  state  definitely  the  universal  canon 
of  this  form  of  the  figured  syllogism,  a  canon  which  to  be  valid 
must  embrace  all  of  the  principles  above  elucidated.  As  such 
a  canon,  we  present  the  following,  to  wit :  Whatever  relations 
of  subject  and  pi'edicate  exist  bettceen  two  terms  and  a  com- 
mon distributed  third  term,  to  which  one  at  least  of  the  former 
is  positively  related,  exist  between  the  terms  themselves.     This 


120  LOGIC. 

axiom  will  be  found  to  include  all  eases  which  fall  under  this 
form  of  the  figured  syllogism,  inasmuch  as  it  implies  all  the  rela- 
tions above  adduced. 


Moods  of  the  Syllogism. 

Every  proposition  must,  as  we  have  seen,  be  universal  or  par- 
ticular, affirmative  or  negative.  When  we  have  designated  the 
propositions  of  a  syllogism  in  order  according  to  their  respective 
quantity  and  quality,  we  have  determined  its  mood.  Thus,  if 
all  the  propositions  are  universal  affirmatives,  we  have  the  mood 
A,  A,  A,  &c.  The  following  extract  from  Dr.  Whately  ex- 
presses all  that  need  be  added  on  this  subject  with  the  excep- 
tion subsequently  stated : 

"  As  there  are  four  kinds  of  propositions  and  three  proposi- 
tions in  each  syllogism,  all  the  possible  ways  of  combining  these 
four  (A,  E,  I,  O)  by  threes,  are  sixty-four.  For  any  one  of 
these  four  may  be  the  major  premise,  each  of  these  four 
majors  may  have  four  different  minors,  and  of  these  sixteen 
pairs  of  premises  each  may  have  four  different  conclusions, 
4X4(=16)  x4  =  64.  This  is  a  mere  arithmetical  calculation 
of  the  moods  without  any  regard  to  the  logical  rules ;  for  many 
of  these  moods  are  inadmissible  in  practice  from  violating  some 
of  those  rules ;  e.  g.  the  mood  E  E  E  must  be  rejected  as  hav- 
ing negative  premises  ;  IOO  for  particular  premises ;  and 
many  others  for  the  same  faults ;  to  which  must  be  added 
I  E  O  for  an  illicit  process  of  the  major  in  every  figure.  By 
examination  then  of  all,  it  will  be  found  that  of  the  sixty-four 
there  remain  but  eleven  moods  which  can  be  used  in  a  legiti- 
mate syllogism, viz. :  AAA;  AAI;  AEE;  AEO;  All; 
AOO;  EAE;  EAO;  EIO;   IAI;  OAO." 

Dr.  Whately  states  that  the  mode  I  E  0  involves  "  an  illicit 
process  of  the  major  in  every  figure."  This  must  be  admitted 
if  we  grant  that  each  figure  alike  has  its  proper  major  and  mi- 
nor terms  and  premises,  which,  as  we  shall  hereafter  see,  is  not 
the  case.  That,  on  the  other  hand,  must  be  regarded  as  an 
allowable  mood  in  which  the  conclusion  necessarily  results  from 


ANALYTIC     OF     SYLLOGISMS.  121 

the  premises  as  presented.  If  we  test  the  mood  under  consider- 
ation by  this  principle,  we  shall  find  that  it  has  the  same  claim 
to  be  regarded  as  allowable  as  any  of  the  others.  That  a  legiti- 
mate and  valid  conclusion  may  be  deduced  from  such  an  ar- 
rangement of  the  terms  and  premises,  will  be  evident  on  a  mo- 
ment's reflection.     For  example : 

Some  X  is  M  ; 

No  Z  is  M  ; 
.-.  No  Z  is  some  X. 
Converse  :  Some  X  is  not  Z. 

No  one  can  deny  that  both  of  the  above  conclusions  directly, 
immediately,  and  necessarily  result  from  the  premises.  This, 
tb*en,  is  an  allowable  mood,  and  we  have  twelve  instead  of 
"  eleven  moods  which  can  be  used  in  a  legitimate  syllogism." 


FIGUKE    OF   THE   SYLLOGISM. 

Form  defined. 

The  figure  of  the  syllogism  is  determined  by  the  relations  of 
the  middle  term  to  the  extremes,  and  the  number  of  the  figures 
will  be  as  the  number  of  the  relations  which  the  terms  admit. 

Number  of  figures  of  the  Syllogism. 

A  moment's  reflection  will  convince  any  one  that  there  are 
three,  and  only  three,  such  relations  conceivable,  to  wit : 

1.  When  the  middle  term  is  the  subject  of  one  extreme  and 
the  predicate  of  the  other. 

2.  When  it  is  the  predicate  of  both  extremes. 

3.  When  it  is  the  subject  of  both. 

We  conclude,  then,  that  there  are  three,  and  only  three,  fig- 
ures of  the  syllogism,  and  they  are  numbered  according  to  the 
order  above  stated.     We  will  give  them  in  their  order : 

I.  II.  III. 

MX;  X  M ;  MX; 

Z  M  ;  Z  M  ;  M  Z  ; 

Z  X  ;  Z  X  ;  Z  X. 


Major  and  Minor  Terms  and  Premises. 

On  a  consideration  of  the  relation  of  the  extremes  to  the  mid- 
dle term  in  the  first  figure,  it  will  be  seen  at  once,  that  the  ex- 
treme which  is  the  predicate  of  the  middle  term,  is,  of  all  the 
terms  employed,  of  the  widest  extension,  including  first  the  mid- 
dle term  and  then  the  other  extreme,  as  included  in  the  middle. 
The  term,  therefore,  which  thus  includes  both  the  others  is 
properly  called  the  major  term ;  and  that  which  is  determined 
first  by  the  middle  term,  and  through  it  by  the  major,  is  called 
the  minor  term.  The  premise  which  contains  the  major  term  is 
called  the  major,  and  that  which  contains  the  minor  term  is 
called  the  minor,  premise.  On  examining  the  other  figures',  it 
will  be  seen  that  in  each  alike  the  middle  term  sustains  precise- 
ly the  same  relation  to  the  extremes.  In  neither  of  these  fig- 
ures, therefore,  is  either  extreme  given  as  a  conception  superior 
or  inferior  to  the  other.  In  the  second  figure  the  middle  term 
is  given  as  alike  superior,  and  in  the  third,  as  alike  inferior  to 
each  of  the  extremes.  In  these  figures,  therefore,  we  have  no 
proper  major  or  minor  terms  or  premises.  To  place  one  as  the 
major  and  the  other  as  the  minor  term  or  premise  is  a  mere  ar- 
bitrary arrangement,  and  tends  to  obscure  rather  than  throw 
light  upon  the  subject. 

Order  of  the  Premises. 

In  the  first  figure  it  is  more  natural  to  place  the  major  premise 
first,  and  then  the  minor ;  though  this  is  by  no  means  univer- 
sally the  case.  The  following  extract  from  "  Thomson's  Laws 
of  Thought"  is  worthy  of  very  special  attention  on  this  subject : 
"  Although  an  invariable  order  for  the  two  premises  and  con- 
clusion, namely,  that  the  premise  containing  the  predicate  of 
the  conclusion  is  first  and  the  conclusion  the  last,  is  accepted  by 
logicians,  it  must  be  regarded  as  quite  arbitrary.  The  position 
of  the  conclusion  may  lead  to  the  false  notion  that  it  never  oc- 
curs to  us  till  after  the  full  statement  of  the  premises ;  whereas 
in  the  shape  of  the  problem  or  question  it  generally  precedes 


ANALYTIC      OF     SYLLOGISMS.  123 

them,  and  is  the  cause  of  their  being  drawn  up.  In  this  point 
the  Hindoo  syllogism  is  more  philosophic  than  that  which  we 
commonly  use.  The  premises  themselves  would  assume  a  dif- 
ferent order  according  to  the  occasion.  It  is  as  natural  to  be- 
gin with  the  fact  and  go  on  to  the  law,  as  it  is  to  lay  down  the 
law  and  then  mention  the  fact. 

"  I  have  an  offer  of  a  commission ;  now  to  bear  a  commission 
and  serve  in  war  is  (or  is  not)  against  the  divine  law ;  therefore 
I  am  offered  what  it  would  (or  would  not)  be  against  the  divine 
law  to  accept. 

"  This  is  an  order  of  reasoning  employed  every  day,  although 
it  is  the  reverse  of  the  technical ;  and  we  cannot  call  it  forced 
or  unnatural.  The  two  kinds  of  sorites  to  be  described  below, 
are  founded  upon  two  different  orders  of  the  premises ;  the  one 
going  from  the  narrowest  and  most  intensive  statement  up  to 
the  widest,  and  the  other  from  the  widest  and  most  extensive 
to  the  narrowest.  The  logical  order  cannot  even  plead  the 
sanction  of  invariable  practice.  Neither  the  school  of  logicians 
who  defend  it,  nor  those  who  assail  it,  take  a  comprehensive 
view  of  the  nature  of  inference.  Both  orders  are  right,  because 
both  are  required  at  different  times ;  the  one  is  analytic,  the 
other  synthetic ;  the  one  most  suitable  to  inquiry,  and  the  other 
to  teaching." 

In  the  second  and  third  figures,  no  order  whatever  of  the 
premises  is  suggested  by  the  relations  of  the  extremes  to  the 
middle  term ;  nor  does  the  validity  of  the  conclusion  depend  at 
all  upon  their  order ;  either  order  is  to  be  employed,  as  occasion 
requires. 


FINAL   ABOLISHMENT    OF   THE   FOURTH   FIGURE. 

Opinions  of  Logicians  upon  the  subjett. 

Logicians  have  commonly  made  four  instead  of  three  syllo- 
gistic figures,  to  wit :  that  in  which  the  middle  term  is  the  sub- 
ject of  the  major  premise,  and  the  predicate  of  the  minor  ;  that 
in  which  it  is  predicate  of  both  extremes;  that  in  which  it  is 


124  LOGIC. 

the  subject  of  both  ;  finally,  that  in  which  it  is  the  predicate  of 
the  major  premise  and  the  subject  of  the  minor. 

When  we  met  with  the  statement  of  Sir  William  Hamilton, 
that  science  requires  the  "  final  abolition  of  the  fourth  figure,"  a 
statement  for  which  he  gives  no  reasons  in  any  of  his  writings 
that  we  have  met  with,  we  at  first  supposed  that  we  had  fallen 
upon  the  statement  of  an  unnecessary  attempt,  if  nothing  more, 
at  simplification  in  the  science  of  logic.  A  careful  examination 
of  the  figure,  however,  together  with  that  of  the  possible  rela- 
tions of  the  extremes  to  the  middle  term,  has  convinced  us  of  the 
truth  and  importance  of  this  statement.  We  fully  agree  with 
this  author  that  there  can  be,  upon  scientific  principles,  but 
"  three  syllogistic  figures,"  and  will  proceed  to  give  our  reasons 
for  that  conviction,  reasons  for  which  we  are  alone  responsible, 
as  they  are  to  us  the  exclusive  result  of  our  own  investigations. 
Our  reasons,  among  others,  are  the  following : 


Our  reasons  for  the  abolition  of  this  Figure. 

1.  The  relations  which  we  have  given  embrace,  as  we  have 
said,  all  conceivable  relations  which  a  single  term  can,  as  subject 
and  predicate,  sustain  to  two  others  in  two  given  propositions, 
to  wit :  the  subject  of  one  extreme  and  the  predicate  of  the 
other;  the  subject  of  both ;  and  the  predicate  of  both  extremes. 
As  but  three  relations  are  conceivable,  science  permits  but  three 
syllogistic  figures. 

2.  The  premises  of  the  fourth  figure  are  in  fact  nothing  but 
those  of  the  first  transposed,  such  transposition  being  allowable 
and  always  understood  as  implying  no  change  of  the  figure  of 
the  syllogism.    For  example : 

All  M  is  X ;  All  X  is  M  ; 

All  Z  is  M.  All  M  is  Z. 

In  the  first  example  we  have  the  premises  of  Barbara  in  the 
first  figure,  and  in  the  second  of  Brumantip  of  the  fourth.  Let 
X  in  the  latter  case  take  the  place  of  Z  and  Z  of  X,  and  every 
one  Mall  perceive  that  we  have  nothing  but  the  premises  of  Bar- 


ANALYTIC     OP     SYLLOGISMS.  125 

bara  changed.  This  is  the  case  in  all  instances  in  the  fourth 
figure.  It  is  contrary  to  all  the  laws  of  science,  therefore,  to 
Buppose  a  new  figure  to  meet  the  case  of  a  mere  change  of  the 
order  of  the  premises. 

3.  In  the  fourth  figure,  as  given  by  logicians  who  retain  it, 
the  scientific  major  term  is  given  as  the  minor  and  the  minor  as 
the  major;  so  of  the  premises.  Take  Brumantip  as  an  illus- 
tration : 

All  X  is  M  ; 

All  M  is  Z  ; 

.-.  Some  Zis  X. 

Who  does  not  perceive  that  Z  is  here  the  superior,  M  the  inter- 
mediate, and  X  the  inferior  conception  ?  Z,  in  the  first  in- 
stance, as  the  superior  conception  contains  M  as  its  inferior  con- 
ception, and  then  M  as  the  superior  contains  X  as  its  inferior 
conception.  Z,  then,  according  to  all  the  laws  of  science,  is  the 
superior  conception,  and  the  consequent  only  proper  major 
term.  X  is  the  proper  minor  ;  and  Z  the  proper  major  term. 
The  same  holds  true  of  all  the  moods  of  this  figure. 

4.  In  this  figure,  as  given  by  logicians,  the  indirect  is,  in  all 
instances,  substituted  for  the  direct  conclusion.  The  direct  con- 
clusion from  the  premises  of  Brumantip,  for  example,  is  "All 
X  is  Z,"  and  not  "  Some  Z  is  X."  If  all  X  is  in  M  and  all  of 
M  in  Z,  then  all  of  X  must  be  in  Z ;  and  this  is  the  direct,  and 
only  direct,  conclusion.  The  proposition,  "  Some  Z  is  X,"  is 
but  the  converse  of  the  inference  which  the  premises  directly 
yield.  The  same  holds  true  of  every  mood  in  this  so  called 
figure.  No  reasons  whatever,  then,  exist  for  retaining  it ;  all 
the  laws  and  principles  of  true  science,  on  the  other  hand,  de- 
mand its  "final  abolition."  It  may  be  often  convenient  to 
change  the  order  of  the  premises  of  the  first  figure,  and  to  state 
its  indirect  conclusion  as  immediately  evident  from  the  premises, 
which  is  often  done.  For  this  reason,  however,  we  should  not 
confuse  the  principles  of  science  by  supposing  a  new  figure. 


SPECIAL   CHARACTERISTICS   AND    CANON   OF  EACH   OF  THE  THREE 
FIGURES. 

On  a  careful  examination  of  the  three  remaining  figures,  we 
shall  perceive  that  in  consequence  of  the  peculiar  relations  of 
the  middle  term  to  the  extremes  in  each,  that  each  must  have 
its  peculiar  and  special  characteristics,  and  be  governed  by  laws 
equally  special  and  peculiar.  We  will  take  them  up  in  the 
order  in  which  they  are  numbered : 

FIGURE    I. 

In  the  first  figure,  the  middle  term,  as  the  subject  of  the  ma- 
jor term,  is  determined  by  said  term,  while  it  (the  middle),  as 
the  predicate  of  the  minor,  itself  determines  the  same,  and  in 
the  immediate  conclusion  the  determining  extreme  stands  as 
the  predicate,  and  the  determined  as  the  subject.  In  this  figure 
consequently  we  have,  from  the  relations  of  the  terms  to  each 
other,  our  proper  major  and  minor  terms  and  equally  proper 
major  and  minor  premises.  From  these  facts  the  proper  order 
of  the  premises,  as  well  as  the  relations  of  the  extremes  as  sub- 
ject and  predicate  in  the  conclusion,  become  perfectly  manifest. 
In  this  figure,  also,  for  the  reasons  just  stated,  we  have  one,  and 
only  one,  direct,  immediate,  and  proximately  definite  conclu- 
sion ;  and,  mediately,  the  converse  of  the  same.  As  an  illustra- 
tion of  the  above  statement  let  us  take,  as  an  example,  the 
mood  Barbara : 

All  M  is  X  ; 

All  Z  is  M  ; 
.-.  AllZisX. 
Converse  :  Some  X  is  Z. 

Here  it  will  be  seen  that  we  pass  from  one  extreme  (X)  to 
the  other  (Z),  through  the  middle  term  (M) ;  X  being  given  as 
containing  all  of  M,  that  is,  as  determining  it,  and  M  in  a  simi- 
lar manner  as  determining  Z.  In  the  conclusion,  also,  each 
term  sustains  to  the  other  the  identical  relation  which  it  did  to 
the  middle  in  the  premises  in  which  it  appears.  X  contains  Z, 
that  is,  determines  it,  as  it  did  M  in  the  major  premise ;  and  Z 


ANALYTIC      OF     S.YLLOGISMS.  127 

is  contained  in  X,  that  is,  is  determined  by  it,  as  the  former 
was  by  M  in  the  minor  premise.  The  relations  of  the  extremes 
to  each  other  in  the  conclusion,  also,  are  necessarily  determined 
by  their  relations  to  the  middle  term  in  the  premises  ;  no  other 
order  than  that  which  gives  X  as  the  predicate  and  Z  as  the 
subject  of  the  conclusion,  being  permitted  by  their  relations  in 
the  premises  to  the  middle  term,  through  which  their  relations 
to  each  other,  as  expressed  in  the  conclusion,  are  determined. 
It  is  by  no  arbitrary  arrangement,  therefore,  that  X  is  given  as 
the  major  term,  and  the  premise  containing  it  as  the  major 
premise  ;  and  Z  as  the  minor  term,  and  the  premise  containing 
it  as  the  minor  premise.  From  the  nature  of  the  relations  of 
the  terms  in  the  premises,  also,  but  one  conclusion,  Z  is  X,  is 
directly  and  immediately  given,  and  this  conclusion  is  a  proxi- 
mately definite  one. 

Similar  remarks  are  equally  applicable,  as  a  careful  examina- 
tion will  show,  to  all  the  other  moods  of  this  syllogism.  This 
figure,  therefore,  has  a  special  canon  which  is  the  following, 
to  wit : 

Whatever  relations  of  determining  predicate  and  of  deter- 
mined subject  exist  between  two  terms  and  a  common  dis- 
tributed third  term,  to  which  one  at  least  is  positively  related, 
that  relation  said  terms  immediately,  that  is,  directly,  hold 
to  each  other  ;  and  mediately,  that  is,  indirectly,  its  converse. 

The  Canon  illustrated. 

We  will  now,  as  a  means  of  illustrating  this  canon,  examine 
each  of  the  moods  in  this  figure.  Barbara  has  already  been  suf 
ficiently  elucidated.  We  will,  therefore,  simply  give  an  exam- 
ple of  reasoning  in  this  mood,  without  the  use  of  letters.  The 
case  we  present  is  cited  from  Dr.  Whately,  and  presents  the 
celebrated  argument  of  Aristotle'  (Mh.,  sixth  book),  to  prove 
that  the  virtues  are  inseparable,  viz. : 

"  He  who  possesses  prudence  possesses  all  virtue  ; 
He  who  possesses  one  virtue  must  possess  prudence  ; 
Therefore,  he  who  possesses  one  possesses  all." 


128  i^ogic. 

We  will  give  Celarent  in  both  forms,  to  wit,  with  and  with- 
out the  letters : 

No  M  is  X  ; 
Every  Z  is  M  ; 

.-.  NoZisX. 
Converse  :  No  X  is  Z. 

Whatever  is  conformable  to  nature  is  not  hurtful  to  society ; 

Whatever  is  expedient  is  conformable  to  nature  ; 
Therefore  :  Whatever  is  expedient  is  not  hurtful  to  society  ; 
Converse  :  Whatever  is  hurtful  to  society  is  never  expedient. 

In  both  these  examples  alike  there  is  a  perfect  conformity  to 
the  canon  above  given.  The  term  included  in  or  determined 
by  the  middle  is  the  subject,  and  the  one  excluded  from,  and 
thus  determining  the  middle,  is  the  predicate  of  the  conclusion. 
This  determines  the  character  and  relations  of  the  extremes  and 
of  the  premises  also.  We  will  now  consider  the  two  remaining 
moods,  Darii  and  Ferio. 

All  M  is  X  ;  No  M  is  X  ; 

Some  Z  is  M  ;  Some  Z  is  M  ; 

.'.  Some  Z  is  X.  .-.  Some  Z  is  not  X. 

Converse  :  Some  X  is  Z.  Converse  :  Some  not  X  is  Z  ; 

Or  better,  perhaps  :  No  X  is  some  Z. 

The  remarks  made  above  are  so  obviously  applicable  to  these 
two  moods,  that  we  need  add  nothing  in  particular  with  respect 
to  them.  From  an  inspection  of  the  four  moods  above  given,  it 
will  appear  that  they  present  the  only  possible  combinations  of 
the  premises  according  to  the  immutable  laws  of  this  figure. 
In  this  figure  alone,  also,  can  all  of  the  four  classes  of  proposi- 
tions A,  E,  I,  and  O,  be  proven. 

FIGTJKE    II. 

In  elucidating  the  second  figure,  we  will  first  present  all  its 
allowable  moods,  as  given  in  the  common  treatises  on  logic. 
The  letters  prefixed  will  indicate  the  quantity  of  the  propo- 
sitions : 


ANALYTIC     OF     SYLLOGISMS. 


Cesare. 

Camestres. 

Fesiino. 

Baroko. 

E. 

XisM; 

A.    XisM; 

E.    XisM; 

A.    XisM; 

A. 

ZisM; 

E.   ZisM; 

I.    ZisM; 

0.    ZisM; 

.-.  E. 

Z  is  X,  or, 

.-.E     ZisX,  or, 

.-.0.    ZisnotX, 

or, 

.-.0    ZisnotX, or, 

E. 

XisZ. 

E.   XisZ. 

I.   not  X  is  Z, 

or, 

I.    not  X  is  Z,  or, 

No  X  is  some 

Z. 

No  X  is  some  Z. 

In  this  figure,  as  will  be  readily  perceived,  we  have  in  neither 
extreme  a  determining  predicate  as  we  have  in  the  first.  We 
have  in  each  extreme  alike,  on  the  other  hand,  nothing  but  de- 
termined subjects.  As  a  consequence  we  have  no  proper  major 
or  minor  terms  or  premises,  each  extreme  sustaining  in  these 
respects  precisely  similar  relations  to  the  middle  term.  The  va- 
lidity of  the  conclusion  in  no  sense  depends  upon  the  order  of 
the  premises.  In  the  first  two  moods,  for  example,  we  have  by 
one  order  of  the  premises,  Cesare,  and  by  a  simple  change  of 
the  order  we  have  Camestres.  Nor  can  any  reason  be  assigned 
why  Z  instead  of  X  should  be  held  as  the  minor  term,  or  why 
the  premise  containing  it  should  be  considered  as  the  minor 
premise.  In  the  premises  sometimes  one  and  sometimes  the 
other  term  is  given  as  in  part  or  wholly  included  in,  and  the 
ofher,  in  each  case,  as  in  whole  or  in  part  excluded  from,  one 
and  the  same  term.  By  what  law  of  intellectual  procedure 
should  one  of  the  extremes  be  called  the  major  term  and  its 
premise  the  major  premise,  and  the  other  the  minor  term  and 
its  premise  the  minor  premise  ?  For  the  same  reason  we  have 
no  fixed  law  of  subordination  for  the  extremes  in  the  conclusion. 
We  have,  on  the  other  hand,  in  all  instances  two  conclusions, 
each  connected  with  the  same  distinctness  and  immediateness 
with  the  premises,  to  wit :  "  No  Z  is  X,  or,  no  X  is  Z  ;"  "  Some 
Z  is  not  X,  or,  some  not  X  is  Z."  A  mere  reference  to  the 
moods  of  this  figure  as  above  given,  is  all  that  is  requisite  to 
verify  the  above  statement.  In  Camestres,  for  example,  X  sus- 
tains the  precise  relation  to  M  that  Z  does  in  Cesare,  and  vice 
versa.  The  inference,  then,  "  No  X  is  Z,"  is  just  as  directly 
and  immediately  deducible  from  the  premises,  as  its  converse 
"No  Z  is  X."  The  same  remarks  are  equally  applicable  to  the 
conclusions,  "  Some  Z  is  not  X,"  and  "  Some  not  X  is  Z,"  ob- 


ftnrivaEsiTT] 


130  LOGIC. 

tained  in  Festino  and  Baroko.  If,  for  example,  "  All  X  is  in 
M,"  and  "  Some  Z  is  not  in  M,"  the  conclusion,  "  Some  not  X  is' 
Z,"  as  immediately  follows  as  its  converse,  "  Some  Z  is  not  X." 
The  difference  here  lies  not  in  the  connection  of  the  conclusion 
with  the  premises,  hut  in  the  fact  that  in  one  case  we  have  an 
apparently  affirmative  conclusion  when  we  have  a  negative 
premise.  The  conclusion,  however,  is,  as  far  as  mere  conven- 
tional form  is  concerned  affirmative,  while  in  reality  it  is  nega- 
tive. So  far,  then,  as  this  kind  of  affirmative  propositions  are 
concerned  we  may  have  in  this,  as  we  shall  see  in  Figure  III., 
an  affirmative  conclusion  when  we  have  one  negative  premise. 
What  we  desire  to  call  especial  attention  to,  is  the  fact,  that  this 
conclusion  is  as  directly  and  immediately  deducible  from  the 
premises,  as  its  negative  converse  "  Some  Z  is  not  X."  In  this 
figure,  then,  the  premises  always  yield  with  the  same  distinct- 
ness and  immediateness  two  conclusions.  In  consequence  of  the 
fact,  that  we  have  no  proper  major  or  minor  premises  in  this 
figure,  we  have,  by  a  change  of  the  order  of  the  premises  in  the 
cases  of  Festino  and  Baroko,  two  additional  allowable  moods, 
making  its  real  number  six  instead  of  four. 

Canon  of  this  Figure. 

The  following,  then,  is  the  special  canon  of  this  figure,  to  wit : 
Whatever  relations  of  determined  subject  is  held  by  two  notions 
to  a  common  distributed  thirfl,  with  which  one  is  positively  and 
one  distributively,  that  is,  negatively,  related,  that  relation  these 
conceptions  hold  indifferently  to  each  other. 

In  illustrating  this  canon  we  will  first  take  the  case  of  Cames- 
tres.  In  this  syllogism  X  is  given  as  wholly  agreeing,  and  Z 
as  wholly  disagreeing,  with  a  common  distributed  third  term, 
M,  to  which  both  stand  related  as  determined  subjects.  In 
other  words  they,  as  determined  subjects,  wholly  disagree  in 
their  relations  to  a  common  distributed  third  term.  Similar  re- 
lations of  subject  and  predicate  must  they  sustain  to  each  other ; 
and  the  propositions,  "  No  X  is  Z,"  and  "  Xo  Z  is  X,"  must  be 
held  as  logically  valid.    In  Cesare  X  is  positively  and  Z  nega- 


ANALYTIC      OF     SYLLOGISMS.  131 

tively  related  to  M.  In  all  other  respects,  therefore,  their  rela- 
tions to  each  other  must  be  as  in  Camestres.  In  the  other  syl- 
logisms of  this  figure.  X  is  given  as  wholly  agreeing  or  wholly 
disagreeing  with  M,  and  Z  as  undistributed,  and  as  such  as  sus- 
taining in  each  case  opposite  relations  to  M.  In  other  words, 
in  these  syllogisms  these  terms  as  determined  subjects  partially 
disagree  in  their  relations  to  M.  In  their  relations  as  subject 
and  predicate  to  each  other,  therefore,  they  are  given  as  partial- 
ly disagreeing  with  each  other.  The  canon  includes  every  case 
that  can  fall  under  this  figure. 

FIGURE     III. 


The  following  are 

the  syllogisms  of  this 

figure  as  commonb 

given,  namely : 

Darapti. 

JDimmis. 

Datisi. 

A.   MisX; 

I.    MisX; 

A.    MisX; 

A.   MisZ; 

A.   MisZ; 

I.    MisZ; 

.-.  I.   ZisX,  or, 

.-.  I.   ZisX,  or, 

.-.  I.    ZisX,  or, 

I.   XisZ. 

I.   XisZ. 

I.   XisZ. 

Felapton. 

Bokardo. 

Ferison. 

E.    MisX; 

0.   MisnotX; 

E.   MisX; 

A.   MisZ; 

A.    MisZ; 

I.   MisZ; 

.-.  0.   ZisnotX,  or 

,      .  •.  0.   Z  is  not  X,  or, 

.-.  0.   ZisnotX,  or, 

I.   not  X  is  Z. 

I.   not  X  is  Z. 

I.   not  XisZ. 

In  this  figure  the  middle  is  in  both  premises  alike  the  deter- 
mined subject,  and  not  the  determining  predicate,  as  in  the 
second.  As  one  extreme  determines  the  middle  in  the  precise 
form  that  the  other  does,  we  have  here,  also,  no  proper  major 
and  minor  terms  or  premises.  The  order  of  the  premises  being 
indifferent,  equally  so  is  that  of  the  terms  in  the  conclusion. 
As  each  premise  may  stand  indifferently  as  major  or  minor,  so 
each  extreme  may  be  indifferently  the  subject  or  predicate  of 
the  conclusion.  In.other  words,  as  in  the  second  figure,  so  in 
this,  the  premises  always  yield  with  equal  distinctness  and  im- 
mediateness  two  conclusions,  one  in  which  one  extreme,  and 


another  in  which  the  other  extreme,  is  the  subject.  A  careful 
examination  of  each  of  the  above  moods  will  'perfectly  evince 
the  truth  of  all  these  statements,  and  will  also  show  that,  by  a 
simple  change  of  the  order  of  the  propositions  in  the  case  of  the 
three  last-named  moods,  we  have  three  more  allowable  ones  in 
this  figure. 

Canon  of  this  Figure. 

The  following,  then,  is  the  special  canon  of  this  figure,  to  wit : 
Whatever  relations  of  determining  predicate  any  two  terms 
sustain  to  a  common  distributed  third  term,  to  which  one,  at 
least,  of  the  former  is  positively  related,  those  relations  these 
terms  sustain  indifferently  to  each  other.  The  application  of 
this  canon  is  too  obvious  to  require  any  special  elucidation. 

Note. — In  giving  to  each  figure  an  especial  canon,  we  have 
followed  the  example  of  Kant  and  of  Sir  William  Hamilton. 
Our  statement  of  these  canons  differs,  not  in  thought  but  in 
form,  from  that  found  in  the  writings  of  these  authors. 

Absurdity  of  reducing  the  Syllogisms  of  the  other  Figures  to 
the  first. 

In  the  Intellectual  Philosophy,  page  320-1,  we  stated  years 
ago  our  objections  to  a  practice  common  to  almost  all  treatises 
on  logic,  of  reducing  the  syllogisms  of  the  other  figures  to  the 
first.  We  are  quite  happy  to  find  our  objections  sustained  by 
such  authority  as  that  of  Sir  William  Hamilton.  At  the  time 
we  stated  these  objections  we  had  never  read  or  heard  of  his 
thoughts  upon  the  subject,  and  he,  of  course,  has  never  met 
with  ours.  Our  objections  to  this  practice,  among  others,  are 
the  following : 

1.  The  laws  of  thought  may  be  fully  elucidated  without  any 
reference  to  figure.  This  we  have  already  sufficiently  shown  in 
determining,  wholly  independent  of  any  reference  to  the  figure, 
the  conditions  on  which  all  valid  conclusions  can  be  deduced. 

2.  Figure  itself,  as  Sir  William  Hamilton  observes,  is  "an 
unessential  variation  in  syllogistic  form."     The  middle  term  is 


ANALYTIC     OF     SYLLOGISMS.  133 

just  as  really  and  truly  compared  with  the  extremes,  and  the 
conclusions  thence  deduced  are  just  as  valid,  in  one  figure  as  in 
any  other.  Not  a  solitary  ray  of  light  is  thrown  upon  the  sub- 
ject by  the  reduction.  This  we  have  already  shown  in  the  pas- 
sage in  the  Philosophy  above  referred  to. 

3.  The  science  of  reasoning  is,  consequently,  rather  obscured 
than  elucidated  by  the  process.  The  pupil  expects  light  and 
finds  none  ;  the  disappointment  obscures  rather  than  illumines 
his  vision  of  the  principles  of  the  science. 

4.  The  pupil,  we  remark  finally,  is  actually  deceived  by  the 
process.  He  is  made  to  think  that  the  validity  of  one  syllogism 
depends,  not  upon  the  relations  of  the  extremes  to  the  middle 
term,  relations  found  in  the  syllogism  itself,  but  upon  that  of 
other  relations  found  in  a  syllogism  of  another  and  different 
figure,  whereas  the  reverse  of  all  this  is  in  fact  true.  The  va- 
lidity of  the  process,  in  each  syllogism  alike,  depends  exclusively 
upon  the  relations  to  each  other  of  the  terms  found  in  it. 
These  considerations  are  abundantly  sufficient  to  justify  us  in 
totally  disregarding  the  custom  under  consideration. 


Nature  of  the  conclusions  obtained  in  this  form  of  the  Syllo- 
gism. 

We  have  already  stated  that  in  this  form  of  the  syllogism, 
there  is  in  reality  but  an  approach  towards  the  truth,  that  is, 
the  whole  truth  pertaining  to  the  objects  of  inquiry.  It  may 
be  a  matter  of  no  little  interest  and  importance  to  consider,  for 
a  few  moments,  the  nature  of  the  conclusions  which  we  do  ob- 
tain. What  then  is  the  nature  of  the  agreement  or  disagree- 
ment between  the  subject  and  predicate  really  affirmed  in  said 
conclusions  ?  Suppose  that  in  the  first  figure  we  have  obtained 
the  conclusion,  "  All  or  some  Z  is  X."  That  answer  may  be 
considered  relatively  to  the  principle  of  intension  or  extension. 
In  reference  to  the  former,  the  conclusion  affirms  that  Z  pos- 
sesses the  elements  represented  by  the  superior  conception  X. 
In  reference  to  the  latter,  it  affirms  that  all  or  some  of  the  indi- 
viduals represented  by  the  individual  or  specifical  conception  Z, 


do  belong  to  the  class  represented  by  the  specifical  or  generical 
conception  X.  What  pertains  to  Z  in  other  respects  is  not 
affirmed  or  denied.  So  in  the  negative  conclusion,  "All  or 
some  Z  is  not  X,"  we  simply  ascertain,  that  in  so  far  as  the 
qualities  represented  by  the  conception  M  are  ever  concerned, 
they  differ,  one  having,  and  the  other  not  having,  them.  How 
far  they  may  or  may  not  agree  in  other  respects,  is  not  ascer- 
tained. 

In  the  second  figure,  from  the  fact  that  one  extreme  does,  and 
the  other  does  not,  rank  in  whole  or  in  part  under  a  given  supe- 
rior conception,  we  infer  that  they  therefore  so  far  disagree. 
This  disagreement  pertains  simply  and  exclusively  to  the  quali- 
ties or  class  represented  by  said  superior  conception.  How  far 
they  agree  or  disagree  in  other  particulars  is  not  ascertained. 
Suppose,  for  example,  that  it  has  been  ascertained  that  A  is, 
and  B  is  not,  guilty  of  murder ;  m  other  words,  that  A  is  not  B. 
In  very  many  particulars,  such  as  taking  life  and  intentionally 
doing  it,  and  doing  it  with  the  same  weapons,  they  may  agree. 
What  has  been  ascertained  is,  that  relatively  to  the  peculiar 
elements  ^represented  by  the  term  murder,  the  act  of  one  does, 
and  that  of  the  other  does  not,  involve  said  elements.  .  This  is 
the  real  character  of  the  conclusions  obtained  in  this  figure. 

In  the  third  figure,  in  affirmative  propositions,  we  ascertain, 
from  the  fact  that  certain  elements  represented  by  a  certain 
conception  M  belong  to  a  part  of  each  of  the  classes  represented 
by  two  conceptions  Z  and  X,  each  superior  to  M,  that  some  in- 
dividuals ranking  under  each  of  these  superior  conceptions  have, 
either  both  the  whole,  or  one  all,  and  the  other  a  part,  of  the 
qualities  represented  by  M,  and,  therefore,  that  they  so  far 
agree.  The  agreement  ascertained  pertains  exclusively  to  the 
qualities  referred  to.  In  negative  conclusions,  from  the  fact 
that  the  elements  referred  to  do  belong  to  a  part  of  one  class 
and  not  to  a  part  of  another  class,  it  is  affirmed  that  so  far  por- 
tions of  these  classes  do  not  agree  with  each  other.  The  disa- 
greement is  always  specific,  and  pertains  exclusively  to  the  ele- 
ments represented  by  the  inferior  conception  M. 

Such  is  the  character  of  all  the  conclusions  obtained  through 


ANALYTIC      OF     SYLLOGISMS.  135 

this  form  of  the  syllogism.  They  are  always  in  themselves  spe- 
cific and  definite,  but  pertain  only  to  a  part  of  what  really  is 
true. 

Kind  of  arguments  which  approp-iately  belongs  to  the  dif- 
ferent Figures. 

It  may  be  important  to  occupy  some  time  in  considering  the 
forms  of  argument  which  most  properly  belong  to  the  different 
figures  of  the  syllogism. 

All  cases  in  which  the  principle  of  extension  on  the  one  hand, 
and  comprehension  on  the  other,  are  in  equilibrium,  belong,  as 
we  have  seen,  exclusively  to  the  first  figure  ;  and  the  question, 
whether  in  any  given  case  these  relations  do  obtain  ?  may,  in 
all  instances,  be  very  readily  resolved.  In  this  figure  the  minor 
as  a  determined  subject  ranks  under  another  term,  the  middle  ; 
while  said  middle,  as  such  a  subject,  ranks  under,  or  is  excluded 
from,  the  major  term.  This  one  peculiarity  distinguishes  all 
arguments  in  this  figure  from  all  which  pertain  to  the  others. 
Suppose,  for  example,  the  question  to  be  argued  is,  Whether  A 
in  a  certain  act,  taking  the  life  of  B,  was  guilty  of  murder,  the 
fact  of  taking  the  life  referred  to  being  admitted.  The  advo- 
cate sustaining  the  charge  first  lays  down  the  general  principle, 
that,  in  the  language  of  Coke  and  Blackstone,  unlawfully  killing 
a  human  being  with  premeditated  malice,  by  a  person  of  sound 
mind,  is  murder  (All  M  is  X),  affirms  and  attempts  to  show, 
that  A  killed  B  in  these  very  circumstances  (All  Z  is  M),  and 
hence  infers  that  A,  in  the  act.referred  to,  was  guilty  of  murder 
(All  Z  is  X).  This  is  an  argument  in  the  mood  Barbara.  On 
the  other  hand,  let  us  suppose  that  the  advocate  on  the  other 
side,  after  laying  down  the  principle  that  taking  life  in  self- 
defence  is  not  murder  (Xo  M  is  X),  affirms  and  attempts  to 
prove  that  A  took  the  life  of  B  in  self-defence  (All  Z  is  M),  and 
hence  concludes  that  the  act  referred  to  was  not  murder  (Xo  Z 
is  X).  We  have  in  such  a  case  an  argument  in  the  mood  Ce- 
larent.  The  application  of  the  above  illustration  to  particular 
conclusions,  affirmative  and  negative,  belonging  to  this  mood, 
are  too  obvious  to  require  elucidation. 


Let  us  suppose,  now,  that  it  is  claimed  or  is  likely  to  be,  that 
two  cases  (X  and  Z)  rank  under  one  and  the  same  principle  or 
superior  conception  (M),  and  that  we  wish  to  disprove  that 
assertion.  In  accomplishing  this  object,  Ave  first  show  that,  on 
the  principle  of  intension,  X  contains  all  of  M,  that  is,  as  an  in- 
ferior X  is  contained  under  M,  as  the  superior  conception  (All 
X  is  M) ;  we  then  show  that  Z  has  none  of  these  elements,  that 
is,  as  an  inferior  conception  does  not  rank  under  M  as  its  supe- 
rior (No  Z  is  M) ;  we  hence  deduce  the  conclusion,  "  No  Z  is 
X,"  that  is,  X  and  Z  do  not  rank  under  the  same  principle.  In 
this  case  the  argument  is  in  the  second  figure,  in  the  mood 
Camestres.  If,  on  the  other  hand,  it  was  argued  that  X  is 
wholly  void  of  certain  fundamental  characteristics  which  Z  pos- 
sesses, and  that,  therefore,  X  and  Z  do  not  belong  to  the  same 
class,  or  that  no  Z  is  X,  the  argument  would  be  in  the  same 
figure,  but  in  the  mood  Cesare.  On  the  same  principle,  in  Fes- 
tino  and  Barako  a  partial  disagreement  is  disproved.  Supposs 
it  to  be  maintained,  for  example,  that  the  miracles  recorded  in 
the  Bible  (X),  and  those  claimed  in  behalf  of  other  religions  (Z), 
are  in  all  essential  characteristics  alike,  and,  therefore,  alike  un- 
worthy of  credit ;  that  is,  the  miracles  recorded  in  the  Bible  are 
of  the  same  essential  characteristics  as  those  claimed  in  behalf 
of  other  religions.  The  latter  class  are  wholly  unworthy  of 
credit.  Such,  therefore,  must  be  the  character  of  the  miracles 
chronicled  in  the  Bible,  an  argument  in  the'mood  Barbara.  In 
opposition  to  this,  we  show,  that  the  latter  class  of  events  have 
all  of  them  certain  infallible  marks  of  credibility  (All  X  is  M), 
that  none  of  the  former  class,  in  fact,  have  any  one  of  these  char- 
acteristics (No  Z  is  M),  and  hence  deduce  the  conclusion,  that 
these  two  classes  of  events  do  not  belong  to  the  same  class  at 
all  (No  Z  is  X).  This,  also,  would  be  an  argument  in  the 
second  figure ;  the  figure  whose  special  province  is  such  kind  of 
refutations.  Suppose  once  more  that  we  wish  to  prove  that 
certain  individuals  of  each  of  two  different  classes  have  certain 
common  characteristics,  that  is,  that  each  class  as  the  superior 
conception  contains  under  it,  in  Avhole  or  in  part,  a  common 
conception,  and  that  there  is  consequently  a  partial  resemblance 


ANALYTIC     OF     SYLLOGISMS.  137 

between  the  classes  themselves;  or,  that  while  part  of  one  class 
has  these  characteristics,  portions  at  least  of  the  other  class 
have  them  not,  and  that,  consequently,  there  is  this  partial  disa- 
greement between  these  classes.  Let  us  suppose,  further,  that 
it  is  asserted  that  all  of  these  classes  have  these  characteristics, 
or  that  all  of  one  class  and  none  of  the  other  have  them,  and 
that  we  wish  to  disprove  these  propositions  in  their  universal 
form.  In  all  the  above-named  cases  we  naturally  use  some  ot 
the  modes  of  the  third  figure.  The  argument  will,  in  the  first 
instance,  stand  thus  :  All  of  these  characteristics  do  belong  to 
one  extreme,  and  all  or  a  part  of  the  same  do  or  do  not  belong 
to  the  other,  and,  therefore,  some  of  one  class  are  or  are  not 
like  some  of  the  other ;  that  is,  "  All  of  M  is  in  X,"  and  "  All 
or  some  of  it  is  or  is  not  in  Z,"  and,  therefore,  all  or  some  of  Z 
is  or  is  not  in  X.  When  we  desire  to  prove  the  contradictory 
of  a  universal  proposition,  whether  affirmative  or  negative,  we 
prove  that  some  of  the  one,  at  least,  are,  and  some  of  the  other 
are  not,  in  the  state  referred  to,  and  that,  therefore,  the  univer- 
sal proposition  cannot  be  true.  In  opposition  to  the  universal 
affirmative  proposition  we  show,  that  no  or  some  M  is  not  in  X, 
and  that  all  or  some  M  is  in  Z,  and,  therefore,  some  Z  is  not 
in  X.  In  opposition  to  the  universal  negative  proposition  we 
show,  that  all  M  is  in  X,  and  that  all  or  some  M  is  in  Z,  and, 
therefore,  some  Z  is  in  X.  In  all  such  positive  arguments,  and 
in  all  replies  like  "those  under  consideration,  the  reasoning  is 
commonly  in  the  third  figure ;  for  example,  "  Prudence  has  for 
its  object  the  benefit  of  individuals;  but  prudence  is  virtue, 
therefore,  some  virtue  has  for  its  object  the  benefit  of  indi- 
viduals." This  argument  is  in  Darapti,  and  its  object  is  to 
establish  a  fact  or  principle.  .  Its  form  would  be  the  same  if  its 
object  was  to  refute  the  principle,  that  no  form  of  real  virtue 
has  for  its  object  the  benefit  of  individuals.  Suppose,  for  the 
sake  of  still  further  elucidation,  that  it  is  argued  that  a  certain 
doctrine  cannot  be  true,  and  that  on  account  of  a  certain  diffi- 
culty (M)  which  it  involves.  The  argument  hi  full  stands  thus  : 
No  doctrine  involving  this  difficulty  (M)  can  be  true  (X),  or, 
"  No  M  is  X."     This  doctrine  (Z)  does  involve  this  difficulty 


138  LOGIC. 

(M),  or,  "All  Z  is  M,"  therefore  this  doctrine  (Z)  cannot  be 
true,  or,  "  No  Z  is  X."  To  refute  this  argument  we  have  only 
to  show,  that  some  one  doctrine  which  cannot  be  denied  in- 
volves this  very  difficulty.  The  argument  in  reply  is  in  Da- 
rapti,  and  stands,  when  stated  in  full,  thus :  This  doctrine  (M) 
involves  this  very  difficulty  (X),  or  "  All  M  is  X."  This  doc- 
trine (M)  is  true  (Z),  or,  "All  M  is  Z."  Therefore,  some  doc- 
trine which  is  true  involves  this  very  difficulty,  or  "  Some  Z  is 
X ;"  in  other  words,  this  objection  is  of  no  force  against  any 
doctrine.  By  carefully  reflecting  upon  the  above  illustrations 
the  pupil  will  be  able  to  judge  correctly  in  regard  to  the  figure 
into  which  any  particular  argument  is,  or  should  be,  thrown. 

A  more  brief  view  of  this  subject. 

To  state  the  matter  in  still  fewer  words :  when  the  middle 
term  stands  intermediate  between  the  extremes,  being  inferior 
to  one  and  superior  to  the  other,  then  the  argument  is  in  the 
first  figure.  This  we  believe  is  generally  the  case  when  one 
premise  is  a  general  or  universal  principle.  In  this  figure  we 
always  advance  from  the  minor  term  through  the  middle  to  the 
major  or  superior  conception.  On  the  other  hand,  when  the 
middle  term  is  superior  to  each  extreme,  then  the  argument  is 
in  the  second ;  and  when  it  is  in  the  relation  of  an  inferior  con- 
ception to  each  extreme,  then  the  argument  is  in  the  third 
figure. 

A    SCIENTIFIC    DETERMINATION    OF    THE    REAL     NUMBER    OF    LE- 
GITIMATE  MOODS   IN   THIS   FORM    OF   THE   SYLLOGISM. 

Hitherto,  in  treatises  on  logic,  the  number  of  legitimate  moods 
has  been  given  as  the  result  of  mere  experiment.  Science  de- 
mands that  it  shall  be  shown  that,  from  the  relations  of  the  ex- 
tremes to  the  middle  term,  there  must  be  a  certain  number  of 
legitimate  moods,  and  that  there  can  by  no  possibility  be  any 
more.     This  is  what  we  now  propose  to  accomplish. 


ANALYTIC     OF     SYLLOGISMS.  139 

Conditions  of  valid  deductions  of  any  kind  in  this  form  of 
the  Syllogism. 

The  following,  it  must  be  borne  in  mind,  are  the  immutable 
conditions  of  any  valid  conclusions  in  the  syllogism  as  thus  far 
elucidated:  1.  The  middle  term  must  be  distributed  at  least 
once  in  the  premises.  2.  No  term  must  be  distributed  in  the 
conclusion  which  Avas  not  distributed  in  the  premises.  3.  One 
premise  at  least  must  be  universal.  4.  When  the  conclusion 
is  universal  both  premises  must  be  of  the  same  character 
5.  One  premise,  also,  must  be  affirmative.  6.  When  the  con 
elusion  is  affirmative  both  premises  must  be  affirmative,  and 
when  one  premise  is  negative  the  conclusion  must  be  negative. 
From  these  laws,  which,  as  we  have  already  seen,  cannot  but 
be  valid,  we  must  have  a  certain  definite  number  of  legitimate 
moods,  and  by  no  possibility  can  we  have  any  more.  This  we 
will  now  proceed  to  show. 

Universal  affirmative  conclusions. 

Let  us,  in  the  first  place,  take  a  universal  affirmative  conclu- 
sion. To  have  such  a  conclusion,  each  premise  must  be  both 
universal  and  affirmative.  Unless  X  and  Z  are  both  given  in 
the  premises  as  agreeing  universally  Avith  M,  the  former  cannot, 
from  their  mutual  relations  to  the  latter,  be  affirmed  to  agree 
universally  with  each  other.  Such  an  agreement  as  legitimates 
such  a  conclusion  does  exist,  as  Ave  have  already  seen,  when  the 
whole  of  one  extreme  is  contained  in  the  middle  term,  and  the 
whole  of  said  term  is  contained  in  the  other  extreme.  AAA, 
then,  is  an  allowable  mood. 

Particular  affirmative  conclusions. 

To  have  a  particular  affirmative  conclusion  both  premises 
must  be  affirmative,  and  one  universal,  of  which  the  middle 
term  is  the  subject,  this  being  the  condition  of  its  being  dis- 
tributed in  an  affirmative   proposition.      Now  there  are  but 


140  LOGIC. 

three  possible  forms  in  which  these  conditions  can  -be  fulfilled, 
to  wit :  when  both  premises  are  universal  affirmatives — when 
the  first  premise  is  a  universal,  and  the  second  a  particular, 
affirmative — and,  when  the  first  is  a  particular,  and  the  second 
a  universal,  affirmative.  There  can,  then,  be  but  three  moods 
yielding  such  a  conclusion,  and  there  may  be  just  this  number. 
When  the  middle  term,  for  example,  is  the  subject  of  two  uni- 
versal affirmative  propositions  we  may  have  a  particular  affirm- 
ative conclusion,  and  in  such  a  case  we  can  have  nothing  more  ; 
because  neither  of  the  extremes  are  distributed  in  the  premises, 
and,  consequently,  must  not  be  in  the  conclusion.  If  all  of  M 
is  in  X  and  Z  alike,  then,  "  Some  Z  must  be  in  X."  A  A  I, 
therefore,  is  an  allowable  mood.  So  if  all  of  M  is  in  X,  and 
some  of  Z  in  M,  some  of  Z  must  be  in  X,  and  from  the  relations 
supposed  nothing  more  can  be  inferred.  These  conditions  may 
undeniably  be  fulfilled  when  the  first  premise  is  universal  (A), 
and  the  second  particular  (I),  and  vice  versa.  All  and  I  A  I 
are,  therefore,  allowable  moods.  We  have,  then,  four  allowa- 
ble affirmative  moods  and  can  have  no  more,  to  wit :  A  A  A ; 
A  A  I;   All;   I  A  I. 

Universal  negative  conclusion. 

To  have  a  universal  negative  conclusion  both  premises  must 
be  universal,  and  one  of  them  affirmative  and  one  negative ; 
that  is,  one  extreme  must  be  given  as  agreeing,  and  the  other 
as  disagreeing,  universally  with  the  middle  term.  This  is  possi- 
ble on  two  conditions  only,  to  wit :  when  the  first  premise  is 
affirmative  and  the  second  negative — and  vice  versa.  On  these 
conditions,  also,  we  may  have  a  logically  valid  universal  nega- 
tive conclusion ;  for  if  all  of  X  and  none  of  Z,  or  none  of  X 
and  all  of  Z,  are  in  M,  in  either  case  none  of  Z  can  be  in  X. 
The  moods  E  A  E  and  A  E  E  are  allowable ;  and  this  gives  us 
six  allowable  moods — four  affirmative  and  two  negative. 


ANALYTIC     OF     SYLLOGISMS.  141 

Particular  negative  conclusions. 

A  particular  negative  conclusion  requires  that  one  premise  be 
affirmative  and  the  other  negative,  and  that  one  at  least  shall 
be  universal.  These  conditions  are  fulfilled:  1.  "When  both 
premises  are  universal,  and  the  first  is  affirmative  and  the 
second  negative,  and  vice  versa  ;  that  is,  A  E  O  and  E  A  O  are 
possible  moods.  2.  When  the  first  premise  is  a  universal  af- 
firmative and  the  second  a  particular  negative,  and  vice  versa, 
to  wit :  A  O  0  and  O  A  O.  3.  When  the  first  premise  is  a 
universal  negative  and  the  second  a  particular  affirmative,  and 
vice  versa  ;  that  is,  E  I  O  and  I  E  O.  These  it  will  be  seen  are 
the  only  possible  arrangements  of  the  premises  consistent  with 
the  necessary  conditions  before  us,  and  present  the  only  possi- 
ble number  of  moods  when  the  conclusion  is  a  particular  nega- 
tive. The  only  question  which  now  arises  is  this :  Are  all  of 
these  allowable  moods  ?  We  affirm  that  they  are,  and  will  now 
proceed  to  verify  this  affirmation. 

Every  one  Avill  perceive  that  when  both  premises  are  univer- 
sal, one  affirmative  and  the  other  negative,  and  one  extreme  is 
the  predicate  of  the  affirmative  premise,  and  consequently  not 
distributed,  that  this  term  must  be  in  the  conclusion  the  subject 
of  a  particular  proposition.  Otherwise  we  should  have  an  illicit 
process  of  said  term.  In  such  a  case,  however,  such  a  conclu- 
sion (a  particular  negative)  must  be  logically  valid ;  because, 
when  none  of  M  is  in  X  and  all  of  M  is  in  Z,  the  part  of  Z  con- 
taining M  cannot  be  in  X,  and  the  proposition  "  Some  Z  is  not 
X,"  will  hold  true ;  and  this  conclusion  is  equally  valid,  what- 
ever the  order  of  the  premises  may  be.  A  E  O  and  E  A  O, 
therefore,  are  valid  moods. 

For  equally  obvious  reasons,  the  moods  A  O  O  and  O  A  O 
must  be  valid.  If  all  X  is  in  M  and  some  of  Z  is  not  in  M,  then 
some  of  Z,  the  part  not  contained  in  M,  cannot  be  in  X ;  and 
this  will  hold  equally  true,  whether  the  affirmative  or  negative 
premise  be  stated  first,  that  is,  A  O  O  and  0  A  O  are  allowable 
or  valid  moods. 

The  validity  of  the  mood  E  I  O  is  self-evident.     If  none  of  M 


142  LOGIC. 

is  in  X  and  some  of  M  is  in  Z,  then  the  part  of  Z  containing 
this  part  of  M  cannot  be  in  X,  and  the  proposition,  "  Some  Z  is 
not  X,"  is  valid.  That  is,  the  mood  E  I  O  is,  and  must  be, 
allowable.  The  same  conclusion,  as  we  have  before  shown,  fol- 
lows, when  the  order  of  the  premises  is  reversed,  and  I  E  0 
must  also  be  held  as  an  allowable  mood. 


The  number  of  Moods. 

We  have,  then,  twelve  allowable  moods,  and  we  can  have  no 
more,  to  wit,  four  affirmative  and  eight  negative  ones.  We 
will  now  give  them  in  their  proper  order :  AAA;  A  A  I ; 
All;  IAI;  AEE;  EAE;  AEO;  EAO;  AOO; 
OAO;EIO;    IEO. 

SIMILAR    DETERMINATION   OF   THE    NUMBER    OF   MOODS    IN   EACH 
FIGURE. 

We  will  now  attempt  a  similar  determination  of  the  number 
of  legitimate  syllogisms  in  each  figure,  keeping  distinctly  in 
view  the  six  conditions  above  stated,  of  deducing  any  valid  in 
ferences  of  any  kind. 

/Syllogisms  allowable  in  the  first  Figure. 

To  have  affirmative  conclusions  of  either  kind  in  the  first 
figure,  the  major  premise  must  be  a  universal  affirmative. 
Otherwise  the  middle  term  would  not  be  distributed  at  all. 
The  minor  premise,  also,  must  be  affirmative,  and  consequently 
a  universal  or  particular  affirmative.  If  the  minor  premise  is 
universal,  the  conclusion  must,  as  we  have  already  seen,  be  uni- 
versal also.  If  it  is  particular,  the  conclusion  is  particular,  and 
no  other  is  allowable.  We  have  then,  in  this  figure,  two  allow- 
able syllogisms  with  affirmative  conclusions,  to  wit,  Barbara  and 
Darii,  and  we  can  have  no  more. 

To  have  a  universal  negative  conclusion  both  premises  must 
be  universal,  one  affirmative  an  1  the  other  negative,  and  both 


ANALYTIC     OF     SYLLOGISMS.  143 

terms  distributed  in  the  premises,  both  being  distributed  in  the 
conclusion  also.  These  conditions  can  be  fulfilled  only  when  the 
major  premise  is  a  universal  negative  proposition,  and  the  minor 
a  universal  affirmative.  If  the  major  premise  was  affirmative, 
the  major  term  would  be  undistributed,  and  we  would  have  no 
negative  conclusion  at  all.  We  can  have,  then,  in  this  figure, 
but  one  syllogism  whose  conclusion  is  a  universal  negative  one, 
to  wit,  Celarent. 

To  have  a  particular  negative  conclusion  in  this  figure,  the 
major  premise  must  be  a  universal  negative,  and  the  minor  a 
particular  affirmative.  If  the  major  premise  was  not  negative, 
the  major  term  would  not  be  distributed,  and  we  should  have 
an  illicit  process  of  that  term  in  the  conclusion.  If  said  premise 
was  not  universal,  the  middle  term  would  not  be  distributed,  and 
we  could  have  no  conclusion  of  any  kind.  If  the  minor  premise 
was  not  a  particular  affirmative  proposition,  the  conclusion  would 
be  universal,  and  not  particular.  But  one  syllogism  having  a 
particular  negative  conclusion  is  possible  in  this  figure,  to  wit, 
Ferio.  In  the  first  figure,  then,  there  are  four,  and  only  four, 
allowable  moods,  to  wit,  Barbara,  Darii,  Celarent,  and  Ferio. 

MOODS    OR    SYLLOGISMS   ALLOWABLE   IN   THE   SECOND   FIGURE. 

The  second  figure  yields  none  but  negative  conclusions.  To 
have  a  universal  negative  conclusion  one  premise  must  be  a  uni- 
versal affirmative,  and  the  other  a  universal  negative,  proposi- 
tion. When  we  have  such  propositions,  the  middle  term  will 
be  distributed  in  the  negative  premise,  and  each  extreme  in  its 
own  premise,  the  extremes  being  the  subjects  of  universal  prop- 
ositions. As  these  conditions  are  fulfilled,  whatever  the  order  of 
the  premises  may  be,  we  have  two  moods  of  this  kind,  to  wit  : 
one  when  the  major  is  affirmative  and  the  minor  negative,  and 
one  when  this  order  is  reversed ;  that  is,  Cesare  and  Camestres 

We  have  a  particular  negative  conclusion  when  the  affirma- 
tive premise  is  particular,  viz.,  Festino  and  Fisteno,  according 
to  the  order  of  the  premises.  So,  also,  when  the  affirmative 
premise  is  universal  and  the  negative  particular  we  have  two 


moods,  according  to  the  order  of  the  premises,  to  wit :  Baroko 
and  Borako. 

There  are,  then,  in  this  figure,  six  allowable  moods ;  two  with 
universal,  and  four  with  particular  negative,  conclusions. 

ALLOWABLE   MOODS    IN   THE   THIRD   FIGURE. 

The  third  figure,  as  we  have  already  seen,  yields  only  partic- 
ular conclusions.  To  have  affirmative  conclusions,  one  of  the 
premises  must  be  universal ;  else  the  middle  would  not  be  dis- 
tributed. Now  there  are  but  three  conceivable  relations  of  the 
premises  which  will  yield  an  affirmative  conclusion,  to  wit : 
when  both  premises  are  universal  affirmatives  (dArAptl)  ; 
when  the  first  premise  is  a  universal,  and  the  second  a  par- 
ticular, affirmative  (dAtlsI) ;  and,  when  the  first  is  a  particu- 
lar, and  the  second  a  universal,  affirmative  (dlsAmls).  All 
these  are  legitimate  moods,  because  that  in  these  the  middle 
is  distributed,  and  no  term  is  distributed  in  the  conclusion,  and 
none  were  distributed  in  the  premises. 

We  may  have  particular  negative  conclusions  on  the  follow- 
ing conditions :  when  both  premises  are  universal,  one  negative 
and  the  other  affirmative  (fElAptOn  and  fAlEptOn) ;  when  one 
premise  is  a  universal  affirmative  and  the  other  a  particular  neg- 
ative (bOkArdO  and  bAkOrA) ;  and,  when  one  premise  is  a 
universal  negative  and  the  other  a  particular  affirmative  (Ferison 
and  Fireson).  This  gives  us  nine  moods  in  this  figure,  making 
just  nineteen  in  the  three  figures.  If  we  subtract  those  which 
result  from  merely  a  change  of  the  order  of  the  premise,  and  in 
which  the  extreme  in  the  first  premise  is  made  the  subject  of 
the  conclusion — moods,  consequently,  which  must  be  regarded 
as  in  themselves  valid,  but  practically  useless — the  number  will 
be  reduced  to  fourteen,  five  affirmative  and  nine  negative  syllo- 
gisms, all  of  which  are  expressed  in  the  following  fines  : 

"  Fig.  1.—  bArbArA,  cElArEnt,  dArll,  fErlO  que,  prioris. 
Fig.  2.— cEsArE,  cAmEstrEs,  fEstlnO,  bArOkO,  secundas. 
Fig.  3.— Tertia,    dArAptl,    dlsAmls,    dAtlsI,    fElAptOn,    bOkArdO, 
fErlsO,  habet." 


ANALYTIC     OF     SYLLOGISMS.  145 

Note. — The  conclusions  resulting  from  the  moods  fEstlnO 
and  bArOkO  in  the  second,  and  from  fElAptOn,  fErlsO,  and 
bOkArdO  in  the  third  figure,  by  a  change  of  the  order  of  the 
premises,  may  be  given  in  a  still  different  form,  to  wit : 

Some  X  is  M  ;  Some  X  is  not  M  ; 

No  Z  is  M  ;  All  Z  is  M  ; 

.-.  No  Z  is  some  X  ;  or,  .-.  No  Z  is  some  X  ;  or, 
Some  X  is  not  Z.  Some  X  is  no  Z. 

All  M  is  X  ;  All  M  is  X  ; 

.  No  M  is  Z  ;  Some  M  is  not  Z  ; 

.•.  No  Z  is  some  X  ;  or,  .\  No  Z  is  some  X  ;  or, 
Some  X  is  not  Z.  Some  X  is  no  Z. 

Feriso  has  been  given  before.  The  form  given  in  this  note 
will  be  seen  to  be  the  preferable  one. 


II.  That  department  of  the  figured  syllogism  in  which 

THERE  IS,  NOT  ONLY  IN  NEGATIVE  BUT  IN  AFFIRMATIVE 
PROPOSITIONS,  THE  DISTRIBUTION  OF  THE  PREDICATE  AS 
WELL    AS    OF    THE    SUBJECT. 

We  now  advance  to  a  consideration  of  the  second  depart- 
ment of  our  present  subject,  the  figured  syllogism,  to  wit :  that 
department  of  it  in  which  there  is,  or  may  be,  not  only  in  nega- 
tive, but  equally  in  affirmative  propositions,  a  distribution  of  the 
predicate  as  well  as  of  the  subject.  The  reason  why  universal 
negative  propositions  distribute  both  terms  is  the  fact,  that  in 
such  propositions  the  terms  are  compared  throughout  their 
whole  extent.  Whenever  such  comparison  occurs  in  affirmative 
propositions,  and  from  the  nature  of  the  case,  must  be  so,  then 
there  is  the  same  distribution  of  subject  and  predicate  in  one 
class  of  propositions  as  in  the  other.  Now  there  is  an  exceed- 
ingly numerous  class  of  propositions  in  which  such  distribution 
occurs,  and,  from  the  character  of  the  relations  of  the  subject 
and  predicate,  must  occur ;  relations  which  can  readily  be  des- 
ignated, and  thus  presented  as  criteria  to  distinguish  this  class 
from  those  in  which  no  such  distribution  obtains.  The  reason, 
7 


146  LOGIC. 

and  only  reason,  why  the  predicate  as  well  as  siibject  is  not 
always  distributed  in  universal  affirmative  propositions  is  the 
fact  that,  in  a  large  part  of  them,  those  which  we  have  consid- 
ered, the  predicate  is  a  superior  and  the  subject  an  inferior  con- 
ception ;  the  sphere  of  the  latter  being  less  than  that  of  the 
former.  In  all  cases,  therefore,  where  the  terms  of  the  proposi- 
tion are  not  thus  related,  there  we  should  expect  to  find  both 
alike  distributed,  and  that  upon  the  same  principles.  "We  will 
now,  though  at  the  expense  of  repeating  something  already 
presented  in  another  connection,  proceed  to  classify  the  propo- 
sitions, which,  whether  affirmative  or  negative,  distribute  the 
predicate  as  well  as  the  subject. 

Among  these  we  notice  the  following : 

Propositions  of  this  kind  classified. 

1.  Substitutive  judgments,  those  in  which  the  predicate,  by 
another  set  of  words  defines  the  subject ;  as,  for  example, 
"Common  salt  is  chloride  of  lime,"  "A  triangle  is  a  figure 
bounded  by  three  straight  lines,"  &c.  The  converse  of  such 
propositions  is,  "  Chloride  of  lime  is  common  salt,"  and,  "  A 
figure  bounded  by  three  straight  lines  is  a  triangle."  And  the 
reason  why  conversion  is  simple  in  such  cases  is,  that  both  terms 
alike  are  distributed. 

2.  Quantitive  judgments  of  that  class  in  which  the  subject 
and  predicate  are  compared  quantities  with  reference  to  the 
ideas  of  equality  and  difference,  and  in  which  one  is  affirmed  to 
be  equal  to,  greater,  or  less  than  the  other.  If  X  =  Z,  Z=X. 
If  X  is  greater  or  less  than  Z,  Z  is  correspondingly  less  or 
greater  than  X.  In  all  such  relations  both  the  subject  and 
predicate  are  alike  distributed,  and  from  the  nature  of  the  rela- 
tions it  must  be  so. 

3.  Numerical  judgments,  those  in  which  the  subject  and 
predicate  are  numerically  compared  with  each  other ;  as  in  the 
judgments,  6+4  =  10,  X  numerically  =Z,  &c.  In  all  such 
judgments  the  same  laws  of  distribution  govern  both  subject 
and  predicate. 


ANALYTIC     OF     SYLLOGISMS.  147 

4.  Correlative  judgments,  those  in  which  the  subject  and 
predicate  are  correlative  terms,  and  affirm  such  correlation  ;  as, 
"  Cause  and  effect,"  *"  Parent  and  child,"  <fcc.  In  all  such  judg- 
ments, also,  the  same  laws  of  distribution  obtain.  If  X  is  the 
cause  of  Z,  Z  is  the  effect  of  X.  If  X  is  the  father  of  Z,  Z  is 
the  child  of  X,  both  terms  being  equally  distributed  in  the  ex- 
posita  and  converse. 

I  5.  All  judgments,  in  which  the  subject  and  predicate  are  com- 
pared with  reference  to  the  idea  of  likeness  or  unlikeness,  fol- 
low the  same  law  of  distribution  in  respect  to  the  subject  and 
predicate  both.  The  converse  of  the  proposition  X  resembles 
Z,  for  example,  is  not  some  Z  resembles  X,  but  Z  resembles  X, 
and  that  for  the  reason,  that  in  such  propositions,  both  terms 
are  alike  distributed,  and  the  conversion  of  a  universal  affirma- 
tive as  well  as  negative  proposition  is  consequently  simple. 

6.  Proportional  judgments,  also,  follow  the  same  law.  For 
example,  "  Exertions  of  certain  individuals  are  proportional  to 
their  strength ;"  "  The  velocity  of  a  moving  body,  its  matter  be- 
ing given,  is  in  proportion  to  the  impelling  force ;"  "  Momentum, 
velocity  being  given,  is  proportional  to  the  quantity  of  matter-;" 
"A  is  to  B  as  C  is  to  D,"  &c.  In  all  such  judgments  the  subject 
and  predicate  are  compared  throughout  their  wdiole  extent,  and 
therefore,  in  universal  affirmatives  as  well  as  negatives,  both 
terms  are  alike  distributed  and  conversion  is  always  simple. 

7.  "We  notice  but  one  other  class  of  judgments  as  falling 
under  the  same  law  of  distribution  relatively  to  the  predicate, 
those  in  which  the  subject  is  a  generical  (superior),  and  the 
predicate  a  specifical  (inferior)  conception,  and  the  object  of  the 
judgment  is  to  affirm,  that  the  former  class  includes  the  latter. 
For  example,  "Animals  are  men,"  that  is,  "Some  animals = all 
men,"  "  Creatures  (some  creatures)  are  animals  (all  the  species 
called  animals)."  In  such  propositions  the  subject  is  particular 
and  the  predicate  universal.  The  syllogism,  whose  premises 
are  of  this  character,  would,  when  stated  in  full,  read  thus : 

Some  animals  are  men  (all  the  race  of  men) ; 
Some  creatures  are  men  (all  the  race  of  men) ; 
.  \  Some  creatures  are  (some)  animals. 


Here  is  a  valid  syllogism  with  two  affirmative  particular  prem- 
ises as  far  as  the  subject  is  concerned.  The  syllogism  is  valid 
because  the  predicate  is  distributed  and  the  extremes  are  mu- 
tually compared  with  the  same  thing.  For  the  same  reasons 
we  may  have  from  similar  premises  a  particular  negative  con- 
clusion which  must  be  held  as  valid.     Example : 

Some  animals  are  (all)  men  ; 
Some  creatures  are  not  men  ; 
Some  creatures  are  not  (some)  animals. 

The  classification  above  given  will,  we  doubt  not,  be  admit- 
ted to  be  valid  as  far  as  it  goes.  Whether  it  includes  all  judg- 
ments of  the  class  before  us  must  be  determined  by  future  in- 
vestigation. Our  object  has  been  to  indicate  the  existence  and 
character  of  the  class  itself,  and  then  to  determine  the  laws  of 
the  syllogism  when  constituted  in  whole  or  in  part  of  such 
propositions. 


ADDITIONAL    SYLLOGISMS   ILLTTSTEATIVE    OF   THE   ABOVE    CLASSES 
OF   JUDGMENTS. 

We  will  now  present  a  few  additional  syllogisms  illustrative 
of  the  above  classes  of  judgments.  We  shall  give  our  examples 
generally  in  the  second  and  third  figures,  in  which,  in  affirmative 
propositions,  either  the  middle  term  or  the  extremes  are  always 
undistributed  in  propositions  whose  subjects  are  inferior  and 
predicates  superior  conceptions.  For  the  sake  of  convenience 
we  will  use  the  following  signs  adopted  by  Sir  William  Hamil- 
ton, to  indicate  the  nature  of  the  propositions :  A  colon  (:) 
placed  before  a  term  indicates  its  distribution,  and  a  comma  (,) 
its  non-distribution.  Thus,  :  A  means  all  A,  and  ,  A  means 
some  A.  The  following«sign  (=)  placed  between  two  terms  in- 
dicates their  equality,  and  consequently  the  fact  that  both  terms 
are  distributed ;  as,  :  A=B,  means  all  A  equals  all  B.  This 
sign  >  placed  between  two  terms  indicates  that  one  is  greater 
than  ;the  other,  and  that  the  one  towards  which  the  convergent 
is  directed  is  the  less,  and  that  towards  which  the  divergent  is 


ANALYTIC     OP     SYLLOGISMS.  149 

directed  is  the  greater.  Thus:  A>B  means  A  is  greater  than 
B,  and  A<B  means  A  is  less  than  B.  Addition,  subtraction, 
multiplication,  division,  and  proportion  will  be  indicated  by  the 
usual  mathematical  signs  employed  to  express  such  relations. 
Let  us  now  consider  the  following  illustrative  examples : 

1.  Syllogisms  constituted  of  Substitutive  Judgments. 

U.  A  triangle  is  a  figure  bounded  by  three  straight  lines  ; 
U.  A  is  a  figure  bounded  by  three  straight  lines  ; 
C  .*.  A  is  a  triangle. 


2.  Quantitive  Judgments. 

(1.) 

(2.)                                 (3.) 

X=M; 

M=X;                          X>M; 

Z=M; 

M=Z ;                            Z=M  ; 

Z=X. 

.-.  Z=X                        .-.  Z  is  lees  than  X. 

(4.) 

(5.)                                  (6.) 

M<X; 

One  half  X=M  ;                           M=X  ; 

M=Z; 

Z=M;                            M=onehalfZ; 

Z  is  less  than  X.       .-.  Z  is  one  half  X        .-.  Z=twice  X, 

3.  Correlative  Judgments. 

(1.) 

M  is  the  cause  of  X  ; 

M  is  the  cause  of  Z  ; 

,\  Z  is  an  effect  of  the  same  cause  as  X. 

(2.) 

X  is  the  son  of  M  ; 

Z  is  the  son  of  M  ; 

.-.  The  father  of  Z  is  the  father  of  X. 

4.  Judgments  falling  under  t/ie  principle  of  likeness  and  un- 


(1-)  (2.) 

X  resembles  M  ;  M  resembles  X  ; 

Z  resembles  M  ;  M  resembles  Z  ; 

.  Z  resembles  X.  .*.  Z  resembles  X. 


5.  ProportionaUud 

(1-)  (2.) 

A:B::C:D;  C  :  D  :  :  A  :  B; 

A  is  one  half  B  ;  A  is  one  half  B  ; 

.-.  C  is  one  half  D.  .*.  C  is  one  half  D. 

Those  judgments  in  which  the  subject  is  a  generical  and  the 
predicate  a  specifical  conception  have  already  been  sufficiently 
elucidated.  The  validity  of  the  above  syllogisms  will  not  be 
questioned.  Their  validity,  however,  depends  wholly  upon  the 
fact  that,  in  judgments  of  the  above-named  classes,  the  predi- 
cate as  well  as  the  subject  is  distributed. 

Table  of  Logical  Judgments. 

In  the  Analytic  of  Judgments  we  showed,  that  in  addition  to 
the  number  of  judgments  given  in  the  common  treatises  on 
logic,  to  wit,  the  universal  affirmative  (A),  the  particular  affirm- 
ative (I),  the  universal  negative  (E),  and  the  particular  nega- 
tive (0),  we  have  four  additional  ones — the  toto-total  affirma- 
tive, in  which  both  subject  and  predicate  are  distributed  (U) ; 
the  parti-total  affirmative,  in  which  the  subject  is  undistributed 
and  the  predicate  distributed  (Y)  ;  the  parti-partial  negative,  in 
which  both  terms  are  undistributed  (w) ;  and  the  toto-partial 
negative,  in  which  the  subject  is  universal  and  the  predicate 
particular  (?)).  We  have  employed,  in  accordance  with  the 
usage  of  Sir  William  Hamilton,  the  letters  IT,  Y,  and  the  Greek 
letters  w  (omega),  and  r\  (eta),  to  express  these  last  four  propo 
sitions.  This  gives  us  eight  instead  of  four  logical  judgments 
which  may  enter  into  different  processes  of  reasoning.  We 
will  give  this  table  of  judgments,  prefixing  their  respective  signs. 


SIGN. 

XL—  All  X  is  all  Z,  or  X=Z  ; 
A.— All  X  is  some  Z,  or  all  X  is  Z  ; 
I. — Some  X  is  some  Z,  or  some  X  is  Z  ; 
Y.— Some  X  is  all  Z,  or  some  X=Z 


ANALYTIC     OP     SYLLOGISMS.  151 

Negatives. 

SIGN. 

E.— No  X  is  Z,  that  is,  any  Z  ; 
u. — Some  X  is  not  some  Z  ; 
r,. — No  X  is  some  Z  ; 
0. — Some  X  is  no  Z,  not  any  Z. 

Mr.  Thomson,  in  his  "  Laws  of  Thought,"  while  he  adopts 
all  the  other  classes  of  judgments,  rejects  ij  and  w  as  useless, 
though  valid  in  themselves.  In  the  Analytic  of  Judgments  we 
have  indicated  fully  our  views  of  these  judgments,  and  have 
there  given  sufficient  reasons  for  retaining  them. 

Of  opposition  and  conversion  of  Judgments. 

In  the  common  treatises  on  logic,  treatises  in  which  all  forms 
of  judgments  are  included  under  the  four  propositions  A,  E,  I, 
and  O,  E  is  given  as  the  contrary  of  A,  and  O  as  its  contra- 
dictory, and  I  as  its  subaltern.  A,  of  course,  is  given  as  the 
contrary  of  E,  and  I  as  its  contradictory,  and  O  as  its  subaltern, 
while  I  and  O  are  given  as  sub-contraries.  By  increasing  the 
classes  of  judgments  we  have  multiplied  the  forms  of  opposition. 
A  has  the  same  number  of  contraries  as  before,  with  the  addi- 
tion of  *j  and  w,  while  U  and  Y  are  both  alike  inconsistent 
with  A.  The  proposition,  for  example,  "AH  X  is  Z,"  cannot 
be  true,  if  any  of  these  propositions  are  true,  to  wit :  "  No  X 
is  Z,"  "  Some  X  is  not  Z,"  "  No  X  is  some  Z,"  or,  "  Some  X  is 
not  some  Z."  The  proposition,  also,  "All  X  is  Z,"  that  is, 
"  some  Z,"  the  real  universal  affirmative  represented  by  A,  is 
inconsistent  with  the  proposition,  "  All  X  is  all  Z,"  that  is,  (U) 
and  some  X  is  all  Z  (Y).  E  now  has,  for  its  contradictory,  as 
before,  I,  and  for  its  contraries  A,  U,  and  Y.  O  has  for  its  sub- 
contrary  not  only  I  but  Y  also,  and  I  is  the  subaltern  not  only 
of  A,  but  also  of  Y.  These  are  sufficient  to  indicate  the  forms 
of  opposition  which  obtain  among  the  eight  classes  of  judgments 
now  admitted  as  real  and  valid. 

In  regard  to  conversion,  E,  TJ,  I,  and  w  are  each  convertible 
into  itself,  that  is,  the  converse  has  the  same  form  as  the  ex- 


152  LOGIC. 

posita.  A  is  converted  into  Y  and  Y  into  A.  O  is  converted 
into  y\  and  >]  into  O.  A  careful  inspection  of  the  above  table  of 
judgments  will  clearly  evince  the  truth  of  all  these  statements. 


Canon  of  this  form  of  the  Syllogism. 

We  now  advance  to  a  consideration  of  the  canon  of  the  form 
of  the  syllogism  under  consideration.  It  is  this :  Every  concep- 
tion or  term,  agreeing  with  a  certain  common  conception  or 
term,  agrees  with  all  others  that  agree  with  said  conception  or 
term,  and  disagrees  with  all  that  disagrees  with  said  concep- 
tion or  term.  If  A,  for  example,  equals  M,  it  equals  all  other 
objects  that  are  equal  to  31.  The  agreement  or  disagreement 
of  the  extremes  will  always  be  as  their  relations  to  the  common 
or  middle  term. 


SPECIAL   CHARACTERISTICS    OF   THIS   FORM    OF   THE   SYLLOGISM. 

It  would  readily  be  anticipated  that  forms  of  the  syllogism, 
the  terms  of  whose  premises  are  exclusively  constituted  of  infe- 
rior and  superior  conceptions,  would  diner  essentially  from  those 
constituted  of  premises  in  which,  even  in  affirmative  proposi- 
tions, the  predicate  as  well  as  subject  is  distributed.  Let  us 
consider  some  of  the  peculiarities  of  this  second  class  of  forms 
of  the  syllogism,  as  compared  with  those  of  the  other  class. 
Among  these  we  notice  the  following : 

1.  In  the  former  class  a  universal  affirmative  can  be  proved 
only  in  the  first  figure,  while  the  second  gives  us  only  negative, 
and  the  third  only  particular,  conclusions.  When  the  premises 
are  composed  of  propositions  which  distribute  not  only  the  sub- 
ject but  predicate  also,  then  we  have  toto-total  affirmative  con-  . 
elusions  in  all  figures  alike  ;  that  is,  U  may  be  proven  in  each 
of  the  three  figures.  We  will  give  a  syllogism  of  this  class  in 
each  figure : 

TJ.         :  M  is  :  X,  i.  e.       M=X ; 

U.         :  Z  is  :  M,      "         Z=M  ; 

U.  .-.  :  Z  is  :  X,      "    .-.  Z=X. 


ANALYTIC     OF     SYLLOGISMS.  153 

Here  the  syllogism  is  in  the  first  figure.  Let  us  now  see  how 
the  argument  will  ■appear  in  the  other  figures : 

Fig.  2.  Fig.  3. 

:  X  is  :  M,  or  X=M  ;  :  M  is  :  X,  or  M=X ; 

:  Z  is  :  M,  or  Z=M ;  :  M  is  :  Z,  or  M=Z ; 

.-.  :  Z  is  :  X,  or  Z=X.  .-.   :  Z  is  :  X,  or  Z=X. 

Every  condition  requisite  to  a  valid  conclusion,  it  will  readily  be 
perceived,  is  as  fully  met,  in  the  above  examples,  in  one  figure 
as  in  the  other.  We  might  add  here  that  in  each  figure  we 
may  also  have  particular  affirmative  conclusions,  U  I  I  and 
I  U  I,  for  example. 

2.  Another  peculiarity  of  this  form  of  the  syllogism  is,  that 
from  apparently  particular  premises  we  can  have  valid  conclu- 
sions ;  as,  for  example  : 

Some  stones  do  not  resist  the  action  of  the  acids  ; 
Some  metals  resist  the  action  of  the  acids  ; 
.-.  Some  metals  are  not  some  stones  ;  or  better, 

Some  metals  differ  in  their  relations  to  the  acids  from  some  stones. 

This  certainly  is  a  valid  argument,  and  arises  from  the  fact 
that  the  middle  term,  though  the  predicate  of  an  affirmative 
conclusion,  is  distributed.  The  predicate  of  the  conclusion,  as 
well  as  the  subject,  is  particular,  though  the  predicate  of  a  nega- 
tive conclusion. 

3.  Another  peculiarity  of  this  form  of  the  syllogism  is  this, 
that  when  the  subject  of  one  premise  is- particular  we  may  still 
have  a  universal  negative  conclusion.  Take  as  an  illustration 
the  following  mood  in  Y  E  E  : 

Some  M  is  all  X  ; 
No  Z  is  M  ; 
.-.  NoZisX. 

Every  condition  requisite  to  a  valid  argument  is  fulfilled  in  the 
above  syllogism. 

4.  We  mention  but  one  other  peculiarity,  the  fact  that  we 
can  have  in  all  figures  alike,  not  only  universal  affirmative  con- 
clusions, but  also  universal  negatives.     UEE  and  EUE  are 


moods  alike  valid  in  all  the  figures.  It  will  be  noticed  that  in 
each  of  the  propositions  of  each  of  these  moods,  both  terms  are 
distributed.  In  the  mathematics  and  other  kinds  of  reasoning, 
the  above  forms  of  argument  are  continually  occurring. 

III.  The  two  forms  of  the  syllooism  combined. 

It  is  evident  that  the  propositions  of  the  same  syllogism  may 
be  constituted  partly  of  propositions  of  the  first  and  partly  of 
those  of  the  second  class  above  elucidated.  In  other  words, 
one  proposition  may  be  constituted  of.  inferior  and  superior  con- 
ceptions, and  another  of  the  class  in  which,  in  affirmative  and 
negative  propositions  alike,  the  predicate  as  well  as  subject  may 
be  distributed.  In  syllogisms  of  the  first  class  of  affirmative 
propositions,  the  middle  term  must  be  the  subject  of  a  univer- 
sal proposition,  else  it  is  not  distributed.  When  we  have  a 
premise  of  the  second  class,  the  middle,  though  the  predicate  of 
an  affirmative  proposition,  may  be  distributed,  and  the  argu- 
ment still  be  valid.  When  all  the  propositions  are  constituted 
of  the  first  class  of  conceptions  we  have  one  kind  of  syllogisms. 
When  they  are  constituted  of  the  second  class  we  have  still 
another  kind  of  arguments.  When  the  two  classes  of  concep- 
tions are  combined  and  enter  into  the  same  argument,  still 
another  class  of  syllogisms  arises.  The  following  extract  from 
"  Thomson's  Laws  of  Thought"  contains  all  that  need  be  said 
under  this  head.  We  feel  at  liberty  to  make  use  of  this  extract 
for  two  reasons  especially,  to  wit :  1.  It  contains  three  sys- 
tems of  notation  taken  very  properly  from  other  authors.  ■ 
2.  The  system  of  notation  of  which  Sir  William  Hamilton  is 
the  author,  together  with  his  classifications  of  the  moods  of  the 
syllogism,  was  furnished  by  that  author  for  the  special  benefit 
of  the  science  of  logic.  We  might  describe  the  systems  of  no- 
tation in  our  own  language.  This,  however,  would  be  needless, 
as  we  should  only  say  the  same  things  through  a  new  selection 
of  words.  The  difference  in  the  arrangement  of  the  moods  by 
Mr.  Thomson  and  Sir  William  Hamilton,  consists  only  in  the 
omission  of  those  syllogisms  which  arise  from  the  use  of  the 


ANALYTIC     OF      SYLLOGISMS.  155 

judgments  u  and  v\  by  the  latter  author,  and  their  rejection  by 
the  former.  Our  reasons  for  agreeing  with  the  latter  have  al- 
ready been  given.  All  persons  who  would  attain  both  to  a 
theoretical  and  practical  knowledge  of  the  science  of  logic, 
should  render  themselves  perfectly  familiar  with  the  moods, 
syllogisms,  and  systems  of  notation  presented  in  this  extract. 
What  has  gone  before  has  fully  prepared  the  way  for  an  intelli- 
gent acquaintance  with  the  subject  here  presented. 

"  Table  of  all  the  Legitimate  Moods  in  all  Figures. 

The  following  table  is  an  index  of  the  moods  in  which  a 
good  inference  can  be  drawn*  It  is  arranged  according  to  the 
order  in  which  the  vowels  occur  in  the  alphabet,  so  that,  when 
any  mood  has  been  omitted,  as  not  available  for  inference,  the 
eye  can  detect  and  supply  it,  and  the  mind  examine  the  reason 
for  its  omission. 

Some  of  these  moods  exemplify  different  special  rules  and 
theorems  of  logical  writers,  of  which  a  few  are  subjoined. 

FIG.    I.  FIG.    II.  FIG.    III. 

AAA AAI 

AEE 

All All 

AOO  

ADA AUY AUA 

AYI AYY A  YA 

EAE EAE EAO 

EIO EIO ElO 

EI?E EUE EUE 

EYO EYO EYE 

IAI 

IUI IUI IUI 

IYI IYI , 

OAO 

OUO OUO 

OYO  

UAA UAA UAY 

*  Another  table  is  given  below,  with  such  additional  moods  as  contain  the  doubtful  nega- 
tive judgments  n  and  u. 


UEE 

LOGIC. 

uee*: 

UEE 

UII 

UII 

UII 

U  0  0  ....... 

U  0  0 ... 

uoo 

u  u  u ...... . 

uuu 

uuu 

U  Y  Y.. 

UYY 

U  Y  A 

YAA 

Y  A  Y 

YEE 

YEE 

YII 

YOO 

YUY 

YU  A 

YUY 

YYY 

YYI 

Fiq.  I. — A  A  A  and  A  A  I  are  the  only  moods  to  -which  the  dictum  de 
omni  directly  applies — 'Whatever  is  said  of  a  class  may  he  said"  of  a  con- 
tained part  of  the  class.' 

Fig.  I. — A  U  A  is  a  formula  into  which  a  '  perfect  induction'  might  fall, 
where  we  affirm  something  of  a  whole  class,  because  we  have  found  it  true 
of  all  the  individuals  or  species  which  the  class  contains.    Thus  : 
x  y  and  z  are  P ; 
S=x  y  and  z  ; 
.-.  Sis  P. 

Leibnitz  gives  the  formula  '  Cui  singula  insunt,  etiam  ex  ipsis  constitu- 
tum  inest.' 

Fig.  I. — E  A  E  and  E  I  0  are  the  only  moods  to  which  the  dictum  de  nullo 
applies.     '  What  is  denied  of  a  class  must  be  denied  of  any  part  of  the  class.' 
E  U  E  and  U  E  E  in  all  figures.     '  Si  duorum  qua?  sunt  eadem  inter  se 
unum  diversum  sit  a  tertio,  etiam  alterum  ab  eo  erit  diversum.' — Leibnitz. 

Figs.  I.  and  II. — U  A  A.  '  Quod  inest  uni  coincidentium,  etiam  alteri 
inest.' — Leibnitz. 

M=P; 
All  S  is  M  ; 
.-.  All  Sis  P. 

U  U  U  in  all  figures.     '  Qua?  sunt  eadem  uni  tertio,  eadem  sunt  inter  se.' 


A  mode  of  Notation. 

To  be  able  to  represent  to  the  eye  by  figures  the  relation 
which  subsists  in  thought  between  conceptions,  tends  so  greatly 
to  facilitate  logical  analysis,  that  many  attempts  have  been 
made  to  attain  it.  Of  two  important  schemes,  that  of  Euler, 
and  that  which  Sir  William  Hamilton  has  by  improving  made 
his  own,  an  account  will  be  given  hereafter.     The  scheme  now 


ANALYTIC     OF     SYLLOGISMS.  157 

to  be  explained  is  that  which  Lambert  makes  use  of  in  his 
Neues  Organon. 

A  distributed  term  is  marked  by  a  horizontal  line,  with  the 
letter  S,  P,  or  M  attached,  to  denote  that  it  is  the  subject, 
predicate,  or  middle  term  of  the  syllogism  : 


An  undistributed  term  is  marked,  not  by  a  definite  line,  but  by 
a  row  of  dots,  to  show  its  indefiniteness,  thus : 


These  are  the  two  forms  of  quantity  in  which  separate  concep- 
tions may  occur.  But  when  two  conceptions  are  joined  in  a 
judgment,  another  power  as  to  quantity  must  be  represented 
also.  Let  the  judgment  be,  'All  plants  are  organized,'  and  let 
the  lower  line  represent  the  subject  and  the  upper  the  predi- 
cate ;  will  this  representation  convey  the  whole  truth  ? 


P  ... 

S  - 


In  one  point  it  is  inadequate,  that  the  term  '  organized'  is  not 
wholly  indefinite.  We  mean,  indeed,  by  it,  only  some  organ- 
ized things  ;  but  then  one  part  of  it  is  made  definite  by  affirm- 
ing it  of  plants.  We  do  not  know  how  many,  or  what,  indi- 
viduals, come  into  the  conception  '  Some  organized  things'  by 
itself;  but  when  it  occurs  in  this  judgment,  we  are  certain  of 
some  individuals  in  it,  viz.,  those  which  are  '  all  plants.'  This 
we  are  able  to  express  by  a  line  pavtly  definite,  partly  undeter- 
mined, thus : 

P 


Every  affirmative  judgment  may  be  represented  by  a  fine  drawn 
under  another,  the  lower  being  always  the  subject.  Negative 
judgments,  which  express  that  one  conception  cannot  be  con- 
tained under  another,  are  represented  by  two  lines  drawn  apart 
from  each  other,  the  predicate  being  a  little  higher  than  the 
subject,  thus : 


158  LOGIC 

But  in  a  syllogism  there  are  three  terms,  so  that  we  require 
three  lines  to  represent  their  relations  ;  and  the  diagram  thus 
drawn  will  supply  some  important  illustrations  of  the  nature  of 
inference.  Suppose  the  premises  are,  'All  matter  undergoes 
change,  and  the  diamond  is  a  kind  of  matter,'  the  relations  of 
the  three  terms  may  be  thus  exhibited : 

P  .... 


From  this  notation,  besides  the  two  premises  given, 

1.  All  M  is  P, 

2.  All  S  is  M, 

we  may  by  reading  downwards  gather  that 

3.  Some  P  is  M,  and 

4.  Some  M  is  S, 

which  are  in  fact  immediate  inferences  by  conversion  from  each 
of  the  premises  respectively.  But  further,  from  knowing  that 
M  stands  under  P,  and  S  under  M,  we  have  learned  that  S 
stands  also  under  P,  and  this  we  may  express,  leaving  M  alto- 
gether out  of  our  statement, 

5.  All  S  is  P, 

6.  Some  P  is  S, 

the  former  being  the  proper  conclusion  from  our  premises,  and 
the  latter  the  converse  of  the  conclusion. 

Where  our  premise  is  negative,  and  by  the  canon  of  syllo- 
gism one  only  can  be  of  that  quality,  the  notation  will  be 

P 

M 

which  would  be  read  thus : 

No  M  is  P ; 

All  S  is  M  ; 
.-.  No  Sis  P. 

Finally,  every  universal  judgment  of  substitution,  or  U,  may 
be  expressed  by  two  equal  lines : 


ANALYTIC      OF     SYLLOGISMS.  159 

p  __ 

s  __ 

But  when  such  a  judgment  expresses  a  logical  division,  as  '  Or- 
ganized beings  are  either  plants,  brutes,  or  men,'  the  divided 
character  of  the  predicate  may  be  expressed  by  breaking  up  the 
line  which  represents  it,  thus  : 

P x y z 


which  would  be  read,  '  All  S  is  either  x  y  or  z.'  The  contrary 
process,  of  logical  composition,  which  is  used  to  express  induc- 
tion, as  '  Plants,  brutes,  and  men  are  the  only  organized  beings,' 
would  appear  as : 


and  be  read  '  x  y  z  make  up  the  sum  of  P.' — The  reader  will 
find  great  advantage  in  comprehending  the  rules  of  syllogism, 
from  figuring  the  syllogisms  to  which  they  happen  to  apply, 
according  to  these  directions.* 

Equivalent  Syllogisms. 

Though  the  reduction  of  syllogisms,  from  a  so-called  imper- 
fect, to  the  perfect,  figure,  is  no  longer  requisite,  now  that  the 
power  of  the  dictum  de  omni  et  nullo  is  confined  to  the  proper 
limits,  the  relations  of  three  conceptions  can  be  expressed,  com- 
monly, in  more  than  one  syllogism  of  the  same  figure,  and  al- 
ways in  different  figures.  And  the  advantage  of  any  adequate 
system  of  notation  is,  that  it  not  only  represents  to  us  the  syllo- 
gism itself,  which  is  one  way  of  stating  the  mutual  bearing  of 
three  conceptions,  but,  in  making  that  mutual  bearing  visible, 
it  furnishes  the  means  of  stating  it  in  other  syllogisms.  An  ex- 
ample will  illustrate  this : 

'  No  agent  more  effectually  imitates  the  natural  action  of  the 
nerves,  in  exciting  the  contractility  of  muscles,'  than  electricity 

*  This  scheme  of  notation  has  likewise  heen  improved  by  Sir  William  Hamilton,  but  the 
view  in  the  text  is  quite  sufficient  for  our  present  purpose. 


160  LOGIC. 

transmitted  along  their  trunks,  and  it  has  been  hence  supposed, 
by  some  philosophers,  that  electricity  is  the  real  agent  by  which 
the  nerves  act  upon  the  muscles.  But  there  are  many  objec- 
tions to  such  a  view ;  and  this  very  important  one  among  the 
rest :  that  electricity  may  be  transmitted  along  a  nervous  trunk 
which  has  been  compressed  by  a  string  tied  tightly  round  it, 
whilst  the  passage  of  ordinary  nervous  power  is  as  completely 
checked  by  this  process,  as  if  the  nerve  had  been  divided.''* 
This  argument  may  be  thrown  into  the  following  syllogism,  as 
the  most  direct  form  of  statement : 

Electricity  will  travel  along  a  tied  nerve  ; 
The  nervous  fluid  will  not  travel  along  a  tied  nerve  ; 
.-.  The  nervous  fluid  is  not  electricity. 

This  is  a  syllogism  in  the  second  figure,  and  of  the  mood 
A  E  E,  which  will  be  found  in  the  table  in  the  preceding  sec- 
tion, and  is  therefore  a  valid  mood.  The  middle  term  is  the 
conception  '  travelling  along  a  tied  nerve ;'  and  one  of  the  other 
terms  is  under  it,  and  the  other  not,  so  that  they  cannot  agree ; 
and  this  mutual  relation  may  be  conceived  by  the  following 

lines : 

M ■ 


The  question  now  is :  Whether  having  obtained  this  relation, 
we  cannot  find  other  moods,  besides  A  E  E,  Fig.  II.,  in  which 
to  express  it  ? 

As  the  physiologist  is  most  engaged  with  the  parts  and  func- 
tions of  the  animal  economy,  to  him  '  the  nervous  fluid'  would  be 
the  most  prominent  term,  the  subject  of  thought,  and  therefore 
would  very  properly  be  the  subject  of  the  whole  syllogism.  But 
the  same  three  conceptions  would  be  the  grounds  for  arguing : 

The  nervous  fluid  will  not  travel  along  a  tied  nerve  ; 
Electricity  will  travel  along  a  tied  nerve  ; 
.•.  Electricity  is  not  the  nervous  fluid. 

This  is  E  A  E,  Fig.  II.,  which  is  also  a  valid  mood ;  and  it 
would  best  suit  one  who  was  examining  electricity.     It  is  the 

*  Carpenter,  Animal'Physiology,  p.  437. 


ANALYTIC     OF     SYLLOGISMS.  161 

same  as  the  last  statement,  except  that  the  present  is  the  con- 
verse of  the  former  conclusion.  Again,  though  somewhat  less 
naturally,  we  may  state  it, 

Nothing  that  travels  along  a  tied  nerve  can  be  the  nervous  fluid  ; 
Electricity  travels  along  a  tied  nerve  ; 
.•.  Electricity  cannot  be  the  nervous  fluid. 

This  is  E  A  E  of  the  first  figure.  From  what  has  been  said  we 
see  that  the  relations  between  any  three  conceptions  in  our 
mind  are  permanent,  that  the  mode  of  statement  is  not  perma- 
nent, but  may  appear  now  as  one  mode  of  syllogism,  now  as 
another ;  that  the  conditions  which  determine  us  to  one  form 
as  more  natural  than  another  are,  partly,  the  difference  of  ex- 
tension in  the  conceptions,  where  it  is  ascertainable,  partly  the 
greater  prominence 'of  one  conception  in  our  thoughts  at  the 
time,  which  entitles  it  to  be  the  subject ;  that  any  one  of  the 
syllogisms  founded  on  the  conceptions  is  sufficient  to  ascertain 
their  relations  ;  and  that  by  a  scheme  of  notation  we  may  rep- 
resent, not  merely  one  of  the  cognate  syllogisms,  but  the  ground 
of  all  of  them,  from  which  they  can  afterwards  be  drawn  out 
separately. 


Sir  William  Hamilton's  Scheme  of  Moods  and  Figures  of 
Syllogisms. 

A  mode  of  notation  proposed  by  Sir  William  Hamilton  is, 
beyond  doubt,  one  of  the  most  important  contributions  to  pure 
logic  which  has  ever  been  made  since  the  science  was  put  forth  ; 
and  I  am  fortunate  in  being  permitted  to  annex  it.  Its  excel- 
lencies are  :  that  it  is  very  simple  ;  that  it  shows  the  equivalent 
syllogisms  in  the  different  figures  at  a  glance ;  that  it  shows  aa 
readily  the  convertible  syllogisms  in  the  same  figure ;  that  it 
enables  us  to  read  each  syllogism  Avith  equal  facility  according 
to  extension  and  intension,  the  logical  and  the  metaphysical 
whole.  Many  of  the  different  elements  of  the  notation  are  not 
new,  but  the  novelty  lies  in  the  completeness  and  simplicity  of 
the  whole  scheme. 


SIR   WILLIAM    HAMILTON'S   SCHEME   OF   NOTATION. 

Fig.  i.  Fig.  it.  Fic.  hi. 

I  X:^m.M:        m:Z  X__^f;^*».Z  X— .-af-^^.-Z 


[JI  X,^m:M: —ZX ^C— — ^fX— ^ ^ 


[Iff  X_.M.       _,Z  X^_.M;^_,Z  ** M.^^ 

^<~    ^^    ^^ 


Y  X.^M> :Z  X: :Mt »Z  X: :M> :Z 

.  ^^    '^<~,  "^^7 


Z 


r23T  X:^.  .j^; .,Z  X__  -jj;-     IMJE  X__  .flf,— ** 

~x~  :s:  ,"^~ 


z 

XL  T}    _.Jr        „  z X^^ZZZiZ  X,^-.m.— -Z 
XffX:- 


~^<"     ^^~    ^>^" 

tf  X^Tm.  \.,z  X: jM; Z  X ^ z 


X  Balanced  Middle;  Unbalanced  Extremes.     B.  Unbalanced  Middle;   Balanced  Ex 
tremes.    O.  Unbalanced  Middle  and  Extremes. 


ANALYTIC      OF      SYLLOGISMS.  163 

In  this  table  M  denotes  the  middle  term ;  and  X  and  Z  the 
two  terms  of  the  conclusion.  A  colon  ( : )  annexed  to  a  term 
denotes  that  it  is  distributed,  and  a  comma  (,)  that  it  is  undis- 
tributed. Where  the  middle  term  has  a  :  on  the  right  side, 
and  a  ,  on  the  left,  we  understand  that  it  is  distributed  when 
it  is  coupled  in  a  judgment  with  the  term  on  the  right,  and  un- 
distributed when  coupled  with  the  other. 

The  syllogisms  actually  represented  are  all  affirmatives,  be- 
ing twelve  in  each  figure ;  and  the  affirmative  copula  is  the 
line  wm,  the  thick  end  denoting  the  subject,  and  the  thin 
the  predicate,  of  extension.  Thus:  'X  :  e»s»-,  M,'  would 
signify  '  All  X  is  (some)  M.'  In  reading  off"  the  intension,  the 
thin  end  denotes  the  subject. 

But  from  each  affirmative  can  be  formed  two  negative  syl 
logisms,  by  making  each  of  the  premises  negative  in  turn. 
The  negation  is  expressed  by  drawing  a  perpendicular  stroke 
through  the  affirmative  copula;  thus:  Mseww..  .  In  the  nega- 
tive moods  the  distribution  of  terms  will  remain  exactly  the 
same  as  it  was  in  the  affirmatives  from  which  they  were  respec- 
tively formed,  with  some  few  exceptions  in  which  the  conclusion 
has  a  term  distributed  Avhich  was  not  when  it  was  affirmative. 

The  line  beneath  the  three  terms  is  the  copula  of  the  conclu- 
sion ;  and  in  the  second  and  third  figures,  as  there  may  be  two 
conclusions  indifferently,  a  line  is  also  inserted  above,  to  express 
the  second  of  them. 

The  mark  v-*->^-w  under  a  mood  denotes  that  when  the 
premises  are  converted,  the  syllogism  is  still  in  the  same  mood. 

But  a  "^^^^^^  between  two  moods  signifies  that  when  the 
premises  01  either  are  converted,  the  syllogism  passes  into  the 
other. 

The  middle  is  said  to  be  balanced  when  it  is  distributed  in 
both  premises  alike.  The  extremes  or  terms  of  the  conclusion 
are  balanced  when  both  alike  are  distributed,  unbalanced  when 
one  is  and  the  other  is  not. 

According  to  this  scheme  there  are  12  affirmative  moods  in 
each  figure,  and  24  negatives,  or  36  altogether.  All  the  possi- 
ble moods  of  syllogism  are  here  exhibited  ;  but  the  value  of  the 


164 


LOGIC. 


inference  in  some  of  them  is  so  small  that  they  would  never 
actually  be  employed.  For  example,  by  making  negative  the 
first  premise  of  No.  vii.  Fig.  II.  we  have  such  a  syllogism  as : 

Some  stones  do  not  resist  the  action  of  acids  ; 

Some  metals  resist  the  action  of  acids  ; 
.  • .  Some  metals  are  not  some  stones  ; 
where  there  is  undeniably  an  inference,  but  one  which  can 
scarcely  be  said  to  add  to  our  knowledge  of  the  subject  of  it. 
To  facilitate  a  comparison  of  this  table  with  the  former  one 
(p.  155),  its  moods  are  translated  into  equivalent  letters;  and 
an  examination  will  prove  that  every  mood  not  containing  the 
vowel  i)  or  w,  occurs  in  both  tables,  which,  after  deducting  the 
disputed  moods  so  marked,  coincide  in  all  respects. 


FIG. 

Aff 
-U  u  u. . 

I. 

Neg. 
..EUE.. 

Table  of  M 

FIG 

Aff 
U  U  TJ.. 

"oods. 
ii. 

Neg. 
..EUE.... 
UEE 
,0Y» 

FIG. 

Aff. 

....uuu.. 

....A  A  I.. 

m. 

Neg. 
..EUE 

-A  Y  I.. 

UEE 
.  .v  Y  •#.. 

Y  Y  I.. 

UEE 

..n  A  m 

-U  T  Y. . 

AO« 
.  .E  YO.. 

TJYY.. 

YO  * 
.E  YO 

U  A  Y.. 

..EAO 

-A  U  A. . 

UOO 

,.,u?„ 

YTJA.. 

UOO 
.0  U  , 

....ADA.. 

U  ,0 
..v  U  n 

-U  A  A. . 

AE, 
.  .E  AE.. 

TJA  A.. 

YE, 
.E  AE 

....UYA.. 

AE, 
..EYE 

-Y  TJ  Y. . 

TJ  v  v 
..OTJO.. 

YEE 
..,  I  ».. 

ATJY.. 

Y  I  1.. 

U   ,  , 

.,uo 

mi.. 

UOO 
..OUO 

-All.. 

AEE 
.0  I  <*.... 

Yu.   0, 

.m  Y  «..., 

10. 
.E  I  0.... 

.«  U  ».... 
I  E  v 
.0  A  i? 

....A  I  I.. 
....I  A  I.. 
....U  I  I.. 
....I  U  I.. 
A  YA.. 

YEE 

..n  I  o 

-I  Y  I.. 

A  w  m 

..<*  Y  «.. 

I  Y  I. . 

..U    A    0, 

-TJ  I  I.. 

..E  I  0.. 

.....TJ  I  I.. 

I  ,  * 
..E  I  0 

■IUI.. 

TJa,  « 

..«  TJ  &>.. 

I  U  I.. 

Uo.0 

..0)   U  u> 

-AAA.. 

IE, 

YA  A.. 

IE, 
..,  Y  , 

-Y  Y  Y. . 

A  ,  , 
.  .0  YO.. 

..  AYY  . 

Y  v  n 
,Y0 

....Y  A  Y.. 

A  0  , 
..0  AO 

TOO.. 

AOO 

Y,0 

ANALYTIC     OF     SYLLOGISMS. 


Sum  of  all  the  valid  Moods  in  each  Figure. 

THIS  TABLE.  FORMER.  TABLE. 

i.  36  (=12aff.4-24neg.)— 14  weak  neg .= 22. 
ii.  36  (=12aff.+24neg.)— 16  weak  neg.=20. 
in.  36  (=12aff.+24neg.)— 15  weak  neg.=21. 


Euler^s  System  of  Notation. 


Perhaps  the  most  celebrated  plan  of  notation  is  that  of  Eu- 
ler,  as  described  in  his  Lettres  a  une  princesse  d? Allemagne'. 
But,  as  it  only  represents  the  extension  of  the  terms,  and  not 
the  opposite  capacity,  of  intension,  it  is  far  inferior  to  that  which 


has  just  been  described.  The  sphere  of  a  conception  is  repre- 
sented by  a  circle  ;  an  affirmative  judgment  by  one  circle  whol- 
ly or  partly  contained  in  another ;  and  a  negative  by  two  sepa- 
rate circles.  The  judgment  that  '  All  men  are  mortal'  has  the 
effect  of  including  men  in  the  class  of  mortal  beings,  which 
would  be  represented  by  a  small  circle  for  '  men,'  in  a  large  one 
for  'mortal.'  The  annexed  diagram  exhibits  (I)  the  mood 
AAA,  (II)  E  A  E,  (III)  All,  and  (IV)  E  I  O,  all  of  the 
first  figure." 


SIR   WILLIAM   HAMILTON'S    SPECIAL    CANONS    Or   THE   DIFFERENT 
FIGURES. 

We  have,  as  we  have  seen,  a  general  canon  for  the  syllogism 
in  all  its  forms,  and,  at  the  same  time,  a  special  one  for  each 
special  form,  and,  also,  for  each  particular  figure.  The  follow- 
ing are  the  forms  adopted  by  Sir  William  Hamilton,  and  com- 
municated by  him  for  the  benefit  of  the  science  of  logic,  the 
form  adapted  to  each  special  figure  in  all  its  various  modifica- 
tions, to  wit  : 

"  Canon  of  the  First  Figure. 

"  In  as  far  as  two  notions  are  related,  either  both  positively, 
or  the  one  positively  and  the  other  negatively,  to  a  third  notion 
to  which  the  one  is  subject  and  the  other  predicate,  they  are 
related  positively  or  negatively  to  each  other  as  subject  and 
predicate. 

"  Canon  of  the  Second  Figure. 

"  In  as  far  as  two  notions,  both  subjects,  are,  either  each  posi- 
tively, or  the  one  positively,  the  other  negatively,  related  to  a 
common  predicate  notion,  in  so  far  are  those  notions  positively 
or  negatively  subject  and  predicate  of  each  other. 


1 


ANALYTIC     OF     SYLLOGISMS. 


"  Canon  of  the  Third  Figure. 


"  In  as  far  as  two  notions,  both  predicates,  are,  either  each 
positively,  or  the  one  positively  and  the  other  negatively,  related 
to  a  common  subject  notion,  in  so  far  are  those  notions,  positive- 
ly or  negatively,  subject  and  predicate  of  each  other." 


CANONS   AND    DIVERSE   FORMS  OF  THE   FIGURED   SYLLOGISM   ELU- 
CIDATED. 

We  will  now  proceed  to  elucidate  somewhat  the  canons  and 
diverse  forms  of  the  figured  syllogism,  by  the  induction  of  a 
few  examples.     We  will  commence  with  the  mood  U  U  U : 

X  is  :  M,  or  X=M ; 
Z  is  :  M,  or  Z=M  ; 
Z  is  :  X,  or  Z=X. 
Converse.  :  X  is  :  Z,  or  X=Z. 

It  will  be  perceived  on  reflection,  that  in  the  premises  each 
extreme,  together  with  the  middle  term,  is  distributed.  Both 
extremes  are,  consequently,  as  required  by  the  canon,  distribu- 
ted in  the  conclusion.  For  the  same  reasons  the  converse  of  the 
conclusion,  like  the  exposita,  is  a  toto-total  affirmative  proposi- 
tion, "  :  X  is  :  Z."  We  give  the  mood  in  the  second  figure. 
We  might  have  given  it  in  the  first  or  third,  and  the  same  re- 
marks would  be  equally  applicable.  Contrast  with  the  above 
an  example  in  the  mood  Barbara : 

:  M  is  X,  that  is,  some  X  ; 
:  Z  is  M,  that  is,  some  M  ; 
.•.  :  Z  is  X,  that  is,  some  X. 
Converse,  Some  X  is  Z,  or  :  Z. 

In  the  major  premise  X,  being  the  predicate  of  a  toto-partial 
affirmative  proposition,  is  undistributed.  Z  and  M  being  the 
subjects  of  such  propositions  are  both  distributed.  The  pre- 
mises, therefore,  permit  only  a  toto-partial  conclusion,  whose 
converse  is  a  particular  proposition,  or,  rather,  a  parti-total  one, 
"  Some  X  is  Z,  that  is,  :  Z."     Let  us  next  consider  the  mood 


168  LOGIC. 

Y  Y  Y,  which,  for  reasons  hereafter  to  be  stated,  is  allowable 
only  in  the  first  figure  : 

,  M  is  :  X  ; 
,  Z  is  :  M ; 
.-.  ,  Z  is  :  X. 
Converse,  :  X  is  ,  Z. 

In  this  mood  M  and  X,  as  the  predicates  of  parti-total  affirma- 
tive propositions,  are  both  distributed ;  the  latter  in  the  major, 
and  the  former  in  the  minor  premise.  Z,  as  the  subject  of  a 
parti-total  proposition,  is  undistributed.  In  the  conclusion, 
then,  Z  should  be  undistributed  and  X  distributed,  while  Z  is 
the  proper  minor  and  X  the  proper  major  term.  The  former, 
then,  as  the  subject  of  the  conclusion,  should  be  particular,  and 
the  latter,  as  the  predicate  of  the  same,  distributed.  In  other 
words,  the  premises  yield  a  parti-total  affirmative  conclusion, 
"  Some  Z  is  all  of  X,"  with  its  converse,  "  All  X  is  Z,  that  is, 
some  Z."  The  mood  Y  Y  Y  is  allowable  only  in  the  first 
figure  for  these  reasons,  that  in  the  second  figure  both  of  the 
extremes,  and  in  the  third  the  middle  term,  would  be  undis- 
tributed. Let  us  now  contemplate  some  of  the  negative  syl- 
logisms.    We  will  first  notice  the  iYw: 

No  M  is  some  X  ; 

Some  Z  is  all  of  M  ; 

.  \  Some  Z  is  not  some  X. 

In  this  syllogism,  while  M  is  distributed  in  both  premises, 
neither  extreme  is  distributed  at  all.  In  the  conclusion,  conse- 
quently, Ave  have,  on  account  of  the  fact  that  one  premise  is 
negative,  but  a  parti-partial  conclusion,  and  that  conclusion  is 
authorized  by  the  premises.  So,  while  in  the  first  figure  we 
can  have  no  syllogism  in  the  mood  A  O  O,  we  may  have  a  valid 
one  in  A  O  cj.     Example  : 

:  M  is  X  ; 

,  Z  is  not  M  ; 
.•.  ,  Z  is  not  ,  X. 

The  middle  term  is  here  distributed  in  both  premises,  and 
neither  of  the  extremes  in  either  of  the  premises.     For  this  rea- 


(Fig,  1.) 

(Fig.  2.) 

Some  M  is  X  (some  X)  ; 

Some  X  is  M  ; 

No  Z  is  M  ; 

No  Z  is  M  ; 

No  Z  is  some  X. 

No  Z  is  some  X 

ANALYTIC     OF     SYLLOGISMS.  169 

son  we  have,  one  premise  being  negative,  a  valid  parti-partial 
negative  conclusion,  to  wit :  "  Some  Z  is  not  some  X." 

In  the  first  figure  we  have  no  valid  syllogism  in  the  mood 
I  E  O.    In  each  alike,  however,  we  have  one  in  I  E  *j : 

(Fig.  3). 
Some  M  is  X  ; 
No  M  is  Z  ; 
No  Z  is  some  X 

In  all  these  examples  M  is  distributed,  being  either  the  subject 
of  a  universal  or  the  predicate  of  a  negative  proposition.  For 
the  same  reasons  Z  is  distributed,  while  X,  being  the  subject  of 
a  particular  or  the  predicate  of  an  affirmative  proposition,  is  not 
distributed.  The  laws  of  deduction,  therefore,  authorize  a  toto- 
partial  negative  conclusion.  These  examples  are  sufficient  for 
purposes  of  elucidation,  and  will  prepare  the  way  for  a  distinct 
understanding  of  the  whole  subject  as  given  in  the  above  table 
from  Sir  William  Hamilton. 


Proper  sphere  and  application  of  Aristotle's  dictum. 

In  almost  all  treatises  on  logic  the  dictum  of  Aristotle,  the 
dictum  de  omni  et  de  nullo,  has  been  assumed  as  the  universal 
canon  of  the  syllogism  in  all  its  forms.  The  dictum  is  this : 
"Whatever  is  predicated  of  any  term  distributed,  whether 
affirmatively  or  negatively,  may  be  predicated,  in  like  manner, 
of  any  thing  contained  under  it."  "This  rule,"  says  Dr. 
Whately,  "may  be  ultimately  applied  to  all  arguments,  and 
their  validity  ultimately  rests  on  their  conformity  thereto."  In 
reply,  we  would  remark,  that  this  canon  is  applicable  to  argu- 
ments of  the  following  class  only:  1.  Something  must  be  af- 
firmed of  a  class  of  objects;  as,  for  example,  "All  men  are 
mortal."  2.  Some  individual  or  individuals  must  be  given  as 
contained  under  this  class ;  as,  "  John  is  a  man."  3.  The  quali- 
ty affirmed  in  the  first  proposition  of  the  whole  class  must,  as 
a  conclusion,  be  affirmed  of  this  individual ;  as,  "  John  is  mor- 
tal."    In  all  such  cases,  the  terms  are  arranged  according  to 


the  canon  of  the  first  figure.  On  examination  it  will  be  found 
that  the  dictum  is  applicable  to  arguments  only  as  they  are  re- 
duced to  this  figure  ;  and  on  one  condition  then,  that  the  terms 
represent  inferior  and  superior  conceptions.  It  is  not  applicable 
to  the  second  and  third  figures  at  all,  nor  to  any  form  of  argu- 
ment in  which  the  terms  do  not  represent  such  conceptions. 
Because  an  argument  belongs  to  this  figure,  it  does  not  follow 
from  hence  that  the  terms  are  subordinated  one  to  another,  as 
above  stated.     For  example : 

:  M=  :  X; 

:  Z=  :  M ; 
.-.  :  Z=  :  X. 
In  this  syllogism  neither  term  is  given  as  in  any  form  subordi- 
nated to  the  other.  Nothing,  in  the  first  instance,  is  affirmed 
of  a  class  of  objects,  and  no  individuals  are  there  given  as  in- 
cluded under  this  class ;  nor  in  the  conclusion  is  something 
affirmed,  as  required  by  the  dictum,  of  individuals  which  had 
been  previously  affirmed  of  the  class.  Each  term,  on  the  other 
hand,  is  equal  to  every  other.  The  argument  is  valid,  and  in 
the  first  figure.  Yet  the  dictum  is  not  applicable  to  it.  What 
then  is  the  exclusive  and  proper  sphere  and  application  of  this 
dictum  f  We  answer  :  1.  The  dictum  de  omni  is  applicable  to 
the  affirmative  moods  of  this  figure,  when  the  terms,  as  repre- 
senting inferior  and  superior  conceptions,  are  subordinated,  as 
such,  the  one  to  the  other,  that  is,  Barbara  and  Darii.  2.  The 
dictum  de  nullo  is  applicable  only  to  Celarent  and  Ferio.  Thus 
a  dictum  which  has  hitherto  been  considered  as  the  basis  of  all 
valid  reasoning,  is  found  to  be  of  quite  limited  application. 


Section  Y. — The  Conditional  Syllogism. 

A  conditional  syllogism  is  one  whose  major  proposition  is  con- 
ditional, and  whose  minor  together  with  the  conclusion  is  cate- 
gorical.   Example : 

If  the  scriptures  are  not  wholly  false  they  are  entitled  to  respect ; 
They  are  not  wholly  false  ; 
.•.  They  are  entitled  to  respect. 


ANALYTIC      OF     SYLLOGISMS.  171 

When  the  reasoning  does  not  turn  upon  the  hypothesis,  but  a 
hypothetical  conclusion  is  drawn  from  a  hypothetical  premise, 
then  the  reasoning  is  categorical.     Example  : 

If  the  Scriptures  come  from  God  they  are  entitled  to  faith  and  obedience  ; 
If  they  are  not  an  imposture  they  came  from  God  ; 

If,  therefore,  they  are  not  an  imposture  they  are  entitled  to  faith  and  obe- 
dience. 

The  reasoning  here  is  throughout  categorical.  In  the  first 
example,  however,  the  case  is  different.  The  reasoning  in  this 
instance  turns  upon  the  hypothesis,  and  consequently,  a  cate- 
gorical answer  is  deduced  from  a  hypothetical  premise.  This  is 
what  is  meant  by  a  hypothetical  or  conditional  syllogism.  The 
major  premise  in  such  syllogisms  consists  of  two  categorical 
ones,  related  to  each  other  as  antecedent  and  consequent,  and 
so  connected  that  the  truth  of  the  latter  necessarily  follows 
from  that  of  the  former.  The  nature  of  such  propositions  and 
the  conditions  of  their  validity  have  been  already  explained. 
Nothing,  therefore,  need  be  added  in  this  connection  on  this 
subject.  In  the  minor  premise  the  truth  of  the  antecedent  is 
affirmed,  and  in  the  conclusion  the  truth  of  the  consequent  in- 
ferred, or,  the  truth  of  the  consequent  is  denied  in  said  premise 
and  that  of  the  antecedent  denied  in  the  conclusion. 

If  we  should  affirm  the  consequent  or  deny  the  antecedent,  no 
conclusion  could  from  hence  be  deduced.  The  reason  is  ob- 
vious. The  truth  of  the  antecedent  does  not,  in  any  sense,  de- 
pend upon  that  of  the  consequent.  It  may  be  true  that  if  A, 
for  example,  has  a  certain  amount  of  real  estate  he  is  rich. 
From  the  fact  that  he  is  rich,  however,  we  cannot  infer  that  he 
has  any  real  estate  at  all,  for  many  individuals  who  are  rich 
have,  or  may  have,  no  such  possessions.  So  the  truth  of  the 
consequent  does  not  depend  upon  that  of  the  antecedent.  It 
is  true,  that  if  A  has  a  fever  he  is  sick.  He  may  have  no  fever, 
however,  and  yet  be  sick  from  some  other  form  of  disease. 
Hence  the  rule  of  this  form  of  the  syllogism,  that  from  the  af- 
firmation or  admission  of  the  truth  of  the  consequent  or  the  de- 
nial of  the  antecedent,  we  can  infer  nothing. 


172  LOGIC. 

The  case  is  very  different,  however,  where  we  grant  the  truth 
of  the  antecedent  or  deny  that  of  the  consequent.  In  the  first 
case  the  latter  must  be  true,  and  in  the  second  the  former  must 
be  false.  Let,  for  example,  the  following  proposition  be  admit- 
ted as  true,  to  wit :  "  If  A  is  B,  C  is  D."  Suppose  we  admit  the 
truth  of  the  antecedent  and  affirm  A  is  B,  then,  undeniably,  we 
must  admit  the  truth  of  the  consequent  C  is  ~D.  Suppose,  on 
the  other  hand,  that  we  deny  the  consequent,  and  affirm  C  is 
not  D.  In  this  case  we  must  deny  the  antecedent,  it  being 
originally  granted  that  if  A  is  B,  C  must  be  D.  Hence  the. 
two  principles,  that  when  we  admit  the  relation  of  consequence 
between  the  antecedent  and  consequent  in  a  conditional  propo- 
sition, the  following  conclusions  must  be  held  as  valid  in  regard 
to  the  deductions  of  conclusions  in  this  form  of  the  syllogism,  to 
wit: 

1.  If  we  admit  the  antecedent  the  consequent  may  be  inferred 
or  affirmed. 

2.  If  we  deny  the  consequent  we  may  deny  the  antecedent. 
The  former  is  called  the  constructive  or  direct,  and  the  latter 

the  destructive  or  indirect  form  of  reasoning. 

THE   APPROPRIATE   SPHERE    OP   THE   COISTDITIONAL   SYLLOGISM. 

The  question  which  now  demands-  attention,  is  the  appro- 
priate sphere  of  the  conditional  syllogism.  In  all  instances,  as 
we  have  seen,  a  universal  proposition  may  in  such  syllogism  be 
substituted  for  the  hypothetical  premise,  and  the  conclusion 
would  be  perfectly  the  same  and  equally  valid.  The  question 
is,  Under  what  circumstances  is  the  hypothetical  form  of  argu- 
mentation to  be  preferred  to  the  categorical  ?  Among  these 
we  notice,  as  of  special  importance,  the  following : 

1.  When  a  question  is  being  argued  under  circumstances  in 
which  there  is  a  strong  reluctance  to  admit  the  conclusion  which 
we  wish  to  reach,  and  in  which,  consequently,  there  is  a  strong 
likelihood  that  the  evidence,  unless  most  distinctly  apprehended 
in  its  nature  and  bearing,  will  be  resisted.  In  such  circum- 
stances it  is  altogether  best  to  state  the  case,  first  of  all,  in  the 


ANALYTIC     OP     SYLLOGISMS.  173 

conditional  form,  to  wit :  if  such  is  the  state  of  the  case,  such  or 
such  a  conclusion  or  consequent  must  he  admitted.  When  the 
relation  between  the  antecedent  and  consequent  is  too  evident 
to  be  denied,  and  the  evidence  to  be  pi-esented  is  equally  con- 
clusive in  itself,  the  hypothetical  form  of  argument  is  the  most 
conclusive  of  all. 

2.  When  such  prejudice  does  not  exist,  but  the  force  or  bear- 
ing of  the  evidence,  though  perfectly  conclusive  in  itself,  is  not 
likely  to  be  distinctly  perceived,  then,  also,  first  of  all,  to  state 
the  case  in  the  hypothetical  form  is  most  likely  to  secure  the  re- 
sult desired.  Any  one  can  see,  the  speaker  may  state,  that,  if 
such  and  such  things  are  shown  to  be  true,  the  conclusion  must 
be  admitted,  and  this  is  precisely  what  I  design  to  accomplish. 
This,  of  all  things,  is  often  best  adapted  to  secure  a  distinct  ap- 
prehension of  the  nature  and  bearing  of  the  evidence  to  be  pre- 
sented. 

3.  When  we  wish  to  test  the  bearing  of  an  argument  which 
comes  under  a  general  principle,  it  is  often  best  to  state  it  hy- 
pothetically  relatively  to  the  specific  case  under  consideration. 
Instead  of  presenting  the  subject  in  the  universal  form,  "All 
who  do  so  and  so  are  guilty  of  such  and  such  crimes,"  for  exam- 
ple, we  had  better  state  the  subject  in  the  hypothetical  form,  to 
wit :  If  these  individuals  have  perpetrated  such  and  such  spe- 
cific acts,  and  done  so  from  such  and  such  motives,  such  and 
such  is  the  character  of  those  acts.  The  bearing  of  the  argu- 
ment will,  in  such  circumstances,  be  most  distinctly  seen. 

4.  But  one  of  the  most  important  uses  of  the  hypothetical 
syllogism  consists  in  its  judicious  employment  for  the  refutation 
of  false  propositions,  by  showing  that  if  their  truth  be  admitted, 
that  of  others  whose  truth  none  will  have  the  effrontery  to  ad- 
mit, must  be  admitted  also.  The  argument  of  Sir  William 
Hamilton  in  favor  of  the  validity  of  external  perception  for  the 
reality  of  its  object,  presents  an  admirable  example  of  this  use  of 
the  conditional  syllogism.  The  object  of  the  author  is  to  show 
that  the  opposite  doctrine  involves  a  universal  impeachment  of 
consciousness  itself  on  all  subjects  alike,  and  a  consequent  denial 
of  the  possibility  of  real  knowledge  on  any  subject.     The  real 


174  LOGIC. 

argument  presented  is  this,  If  the  validity  of  the  testimony  of 
consciousness  is  denied  in  this  specific  case,  it  is  to  he  denied 
universally.  The  dogma  under  consideration  does  deny  its  va- 
lidity in  this  case,  and,  therefore,  impeaches  it  universally. 
With  these  remarks  special  attention  is  invited  to  the  extract 
referred  to : 

"  In  perception,  consciousness  gives  as  an  ultimate  fact,  a  be- 
lief of  the  knowledge  of  the  existence  of  something  different 
from  self  As  ultimate  this  belief  cannot  be  reduced  to  a 
higher  principle  ;  neither  can  it  be  truly  analyzed  into  a  double 
element.  We  only  believe  that  this  something  exists,  because 
we  believe  that  we  knoxc  (are  conscious  of)  this  something  as 
existing  ;  the  belief  of  the  existence  is  necessarily  involved  in 
the  belief  of  the  knowledge  of  the  existence.  Both  are  origi- 
nal, or  neither.  Does  consciousness  deceive  us  in  the  latter,  it 
necessarily  deludes  us  in  the  former ;  and,  if  the  former,  though 
a  fact  of  consciousness,  be  false,  the  latter,  because  a  fact  of  con- 
sciousness, is  not  true.  The  beliefs  contained  in  the  two  propo- 
sitions : 

"  1st.  I  believe  that  a  material  world  exists, 

"  2d.  I  believe  that  I  immediately  know  a  material  world 
existing,  (in  other  words,)  I  believe  that  the  external  reality  it- 
self is  the  object  of  which  I  am  conscious  in  perception,  though 
distinguished  by  philosophers,  are  thus  virtually  identical."  In 
another  place,  he  adds,  "  In  our  perceptive  consciousness  there 
is  revealed  as  an  ultimate  fact,  a  self  and  a  not-self — each  given 
as  independent — each  known  only  in  antithesis  to  the  other. 
No  belief  is  more  intuitive,  universal,  immediate,  or  irresistible, 
than  that  this  antithesis  is  real  and  known  to  be  real ;  no  belief, 
therefore,  is  more  true. 

"  If  the  antithesis  be  illusive,  self  and  not-self  subject  and  ob- 
ject, Zand  thou,  are  distinctions  without  a  difference;  and  con- 
sciousness, so  far  from  being  '  the  internal  voice  of  our  Creator,' 
is  shown  1 1  be,  like  Satan,  '  a  bar  from  the  beginning.' " 


ANALYTIC      OF     SYLLOGISMS.  175 

Section  VI. — The  Disjunctive  Syllogism. 

A  disjunctive  syllogism  is  one  whose  major  premise  is  a  dis- 
junctive, and  whose  minor  together  with  the  conclusion  is  a 
categorical,  proposition. 

A  disjunctive  proposition  or  judgment  has  already  heen  de- 
fined, as  a  proposition  made  up  of  two  or  more  categorical  ones, 
one  at  least  of  which  must  be  true,  and  the  others  false.  We 
have  also  presented  the  characteristics  of  all  valid  judgments  of 
this  kind.  On  these  topics  nothing  more  need  he  added  in  tliis 
connection. 

In  disjunctive  syllogisms  we  argue  in  either  of  two  directions  : 
from  the  truth  of  one  member  of  the  disjunction  to  the  falsity  of 
the  others ;  or,  from  the  falsity  of  all  but  one,  to  the  truth  of 
that  one.  For  example,  A  is  either  B,  C,  or  D.  It  is  B,  and, 
therefore,  not  C  or  D.  Or,  A  is  B,  C,  or  D.  It  is  not  C  nor  D, 
it  is,  therefore,  B. 

When  the  proposition  to  be  argued  is  a  very  important  one, 
it  may  be  wise  to  adopt  both  forms  of  argumentation  above 
stated  ;  that  is,  first  show  by  one  process  that  the  one  member 
is  true,  and  the  others,  consequently,  false,  and  then,  by  another 
process,  that  these  are  false,  and  that  the  one  under  considera- 
tion, consequently,  must  be  true.  When  the  major  proposition 
in  such  syllogism  is  valid,  either  of  the  forms  of  argument  above 
mentioned  must  be  valid  also. 

Circumstances  in  which  the  Disjunctive  Syllogism  should  be 
used. 

The  following,  at  least,  are  circumstances  where  the  disjunc- 
tive syllogism  may  be  most  successfully  employed  : 

1.  When  we  wish  to  ascertain  or  prove  the  motives  of  an  in- 
dividual in  a  certain  act  or  course  of  conduct,  and  but  a  certain 
number  of  motives,  two  or  more,  are  conceivable  from  the  na- 
ture of  the  case,  and  when  one  of  these  to  the  exclusion  of 
the  others,  must  be  the  real  one.  In  such  circumstances,  it  is 
often  indispensable  to  full  conviction,  and  always  most  favorable 


176  LOGIC. 

to  the  ascertainment  and  establishment  of  the  truth,  to  state  dis- 
tinctly these  different  hypotheses,  and  to  show  that  one  of  them 
must,  and  but  one  can,  be  true.  The  argument  may,  then,  take 
either  of  the  two  courses  above  named,  or  both  united,  and  that 
with  the  greatest  prospect  of  a  satisfactory  issue.  A,  we  will 
suppose,  has  taken  the  life  of  B  under  circumstances  which  ren- 
der it  certain  that  this  was  done  in  sell-defence,  and  the  act  is, 
consequently,  no  legal  crime  whatever ;  or,  with  malice  pre- 
pense, and  is,  therefore,  to  be  regarded  as  murder.  How  im- 
portant to  a  correct  judgment  of  the  facts,  is  a  distinct  appre- 
hension of  the  case  in  the  light  of  these  two  hypotheses.  The 
disjunctive  syllogism  alone  has  place  in  such  cases. 

2.  Suppose  that  the  question  to  be  argued  pertains  to  the  in- 
quiry, What  is  the  cause  or  law  of  a  given  class  of  facts  ?  and 
that,  from  the  nature  of  the  case,  but  a  certain  number  of  hy- 
potheses are  conceivable,  one  of  which,  and  but  one,  to  the  ex- 
clusion of  all  the  others,  must  be  true.  In  all  such- cases,  it  is  of 
the  utmost  importance  to  state  distinctly  these  different  hypoth- 
eses, and  to  show  their  real  relations  as  members  of  the  disjunc- 
tion. In  other  words,  in  all  such  cases,  the  disjunctive  syllogism 
has  place  and  must  be  employed,  if  we  would  argue  with  any 
reasonable  hope  of  success. 

3.  Suppose  that  the  question  to  be  argued  pertains  to  the 
meaning  of  a  certain  document  or  passage.  When  the  words  ad- 
mit of  different  constructions,  or  when  various  constructions  are 
conceivable,  here,  too,  such  constructions  should  be  presented 
as  members  of  the  disjunction  ;  that  is,  it  should  be  shown  that 
such  and  such  constructions  alone  are  conceivable,  and  that  one 
only  can  be  true,  and  that  this  one,  to  the  exclusion  of  the 
others,  must  be  true.  We  are,  then,  best  prepared  to  state  the 
argument  in  favor  of  one,  and  against  the  other,  hypothesis. 
In  all  cases,  in  short,  where  a  case  to  be  argued  admits  of  dif- 
ferent constructions,  and  when  different  constructions  are  put 
upon  it,  it  is  of  the  greatest  importance  to  state  definitely  in  the 
outset  how  many  such  are  conceivable,  and  to  show  that  one, 
to  the  exclusion  of  the  others,  must  be  true.  Here  is  the  ap- 
propriate sphere  of  the  disjunctive  syllogism,  and  within  its 


ANALYTIC     OF     SYLLOGISMS.  177 

sphere  no  other  form  of  argument  can  well  be  substituted  in  its 
place. 

Sectioh  VII. — The  Dilemma. 

A  dilemma  is  a  form  of  the  syllogism  in  which  the  major 
premise  is  a  conditional,  and  the  minor  a  disjunctive,  proposi- 
tion.    Of  this  form  of  the  syllogism  there  are  three  kinds  : 

1.  Where  there  are  in  the  major  different  antecedents,  all 
having  the  same  consequent,  while  in  the  minor  these  ante- 
cedents are  disjunctively  affirmed,  and  in  the  conclusion  the 
common  consequent  is  affirmed.  For  example  :  If  A  is  B,  A  is 
X  ;  and  if  A  is  C,  A  is  X  ;  and  if  A  is  D,  A  is  X.  But,  either 
A  is  B,  A  is  C,  or  A  is  D  ;  therefore,  A  is  X. 

2.  Where  we  have  the  same  antecedent  and  different  conse- 
quents, one  of  which  must  be  false,  and  when  in  the  minor 
premise  we  disjunctively  deny  the  consequents,  and  in  the  con- 
clusion deny  the  antecedents.  If  A  is  B,  C  is  D  ;  and  if  A  is  B, 
E  is  F  ;  and  if  A  is  B,  G  is  H.  But,  either  one  or  the  other  of 
these  consequents  must  be  false  ;  thex-efore,  A  is  not  B. 

3.  When  we  have  several  antecedents,  and  each  a  different  con- 
sequent, and  when  in  the  minor  premise  we  disjunctively  deny 
the  consequents,  and  in  the  conclusion  disjunctively  deny  the 
antecedents,  or  similarly  affirm  the  antecedents  and  consequents. 
If  A  is  B,  C  is  D ;  and  if  E  is  F,  G  is  II.  But,  either  C  is  not 
D,  or  G  is  not  H ;  and,  therefore,  either  A  is  not  B,  or  E  is  not 
F  ;  or  A  is  B,  or  E  is  F  ;  therefore,  either  C  is  D,  or  G  is  H. 

When  we  affirm  the  antecedent,  and  as  a  consequence  infer 
the  consequent,  we  have  what  is  called  the  constructive,  and 
when  we  deny  the  consequent,  and,  therefore,  deny  the  ante- 
cedent, we  have  what  is  called  the  destructive,  dilemma. 

Circumstances  which  require  the  use  of  this  form  of  the  Syl- 
logism. 

We  now  notice  the  circumstances  in  which  this  form  of  the 
syllogism  may  be  employed  to  the  greatest  advantage  : 


178  LOGIC. 

1.  When  several  consequents  are  necessarily  connected  with 
a  particular  dogma  which  we  desire  to  disprove,  consequents  so 
related  to  said  dogma  that  if  it  be  true,  all  these  must  be  ad- 
mitted, but  some  at  least  of  which  are  so  undeniably  self-con- 
tradictory and  absurd,  that  no  one  will  have  the  effrontery  to 
maintain  them.  In  such  circumstances  no  form  of  argument 
can  have  such  force  as  the  syllogism  under  consideration.  So, 
also,  when  the  conduct  of  an  individual  is  such,  that  it  can  be  ex- 
plained in  consistency  only  with  one  of  two  or  more  intentions, 
each  of  which  is  equally  dishonorable  to  himself  and  available 
in  argument  to  his  conviction ;  here,  also,  we  have  a  case  for 
the  dilemma,  a  case  coming  under  the  same  principle  as  that 
above  specified.  In  illustration,  take  the  dogma  of  infidelity, 
that  the  miraculous  events  recorded  in  the  Scriptures  never  oc- 
curred. If  this  dogma  is  true,  then  those  who  professed  to  per- 
form these  miracles  must  have  known  that  they  were  deceiving 
the  world  in  such  pretensions,  and  Christ,  the  prophets,  and 
apostles  must  have  been  gross  impostors  and  deceivers.  If  this 
dogma  is  true,  those,  also,  who  narrated  these  events  must  have 
known  the  falsehood  they  were  palming  upon  the  wTorld,  and 
they,  too,  must  be  held  as  deliberate  deceivers  of  the  grossest 
character.  Once  more  :  if  this  dogma  is  true,  the  enemies  of 
Christ,  his  own  murderers  and  crucifiers  among  others,  must 
have  united  with  his  disciples  and  Christians  generally  in  deceiv- 
ing the  world  in  regard  to  these  events ;  for  they  all  alike  ad- 
mitted the  fact  of  their  occurrence.  But  Some  of  these  neces- 
sary consequences  of  this  dogma  must  be  false,  and  the  dogma 
itself  cannot  be  true.  In  this  case  none  of  the  consequences  re- 
ferred to  can  be  true.  All  that  is  requisite  to  the  destruction  of 
the  antecedent,  however,  is  a  disjunctive  denial  of  these  conse- 
quents. 

2.  .When  we  have  a  number  of  facts  or  principles,  some  of 
'which  must  be  admitted  as  real  or  true,  and  while  each  alike 
stands  necessarily  connected  with  a  conclusion  which  we  desire 
to  establish,  so  connected,  that  if  any  one  of  the  series  be  admit- 
ted, .the  common  consequent  must  be  admitted  also.  Here,  too, 
no  form  of  .argument  can  take  the  place  of  this  one  form  of  the 


ANALYTIC      OF     SYLLOGISMS.  179 

syllogism.  In  many  instances  it  may  happen  that  all  the  facts 
referred  to  are  true.  Yet  if  the  argument  is  made  to  turn  upon 
such  a  broad  claim,  it  may  happen  that  the  conclusion  would 
thereby  he  esteemed  doubtful.  When  there  can  be  no  doubt 
that  some  must  be,  and  while  it  is  undeniable  that  if  any  are, 
true,  the  conclusion  must  be  valid,  the  disjunctive  syllogism 
should  always  be  employed. 

3.  It  not  unfrequently  happens  that  the  advocate  of  a  certain 
dogma  may  be  necessitated  to  take  one  of  two  distinct  positions, 
and  when  each  is  connected  necessarily  with  consequents  abso- 
lutely ruinous  to  his  cause.  A  distinct  statement  of  these  posi- 
tions, together  with  the  necessary  consequents  of  each,  will  often 
render  the  truth  demonstratively  evident.  An  individual  some- 
times, also,  may  be  placed  in  circumstances  where  he  must  act 
in  one  of  two  or  more  specific  directions,  and  when  action  in 
either  direction  would  be  inconsistent  with  his  principles  or  pro- 
fessions. In  nil  such  cases  we  have  the  appropriate  sphere  of 
the  dilemma.  For  example,  "If  this  man  were  wise  he  would 
not  speak  irreverently  of  the  Scriptures  in  jest;  and,  if  he  were 
good,  he  Avould  not  do  so  in  earnest ;  but  he  does  so  either  in 
jest  or  in  earnest,  therefore,  he  is  not  wise  or  not* good."  "If 
^Echines  joined  in  the  public  rejoicings  he  is  inconsistent ;  if  he 
did  not  join  he  is  Unpatriotic  ;  but  he  either  did  or  did  not  join, 
therefore  he  is  either  inconsistent  or  unpatriotic." 


Section  VIII. — The  Deductive  and  Inductive  Syllogisms. 

The  inductive  and  deductive  syllogisms  are  commonly  repre- 
sented as  distinguished  from  each  other  by  the  following  par- 
ticulars. In  the  first,  we  reason  from  the  particular  to  the  gen- 
eral, from  the  individual  to  the  whole  class ;  whereas  in  the  lat- 
ter, wre  reason  from  the  general  to  the  particular,  from  the  class 
to  the  individual.  This  view  of  the  subject  has  evidently  arisen 
from  confounding  the  laws  of  investigation  with  those  of  reason- 
ing. In  the  former  process  individual  facts  are  investigated  as 
preparatory  to  illation  or  induction  proper.     We  thus  investi- 


180  LOGIC. 

.gate  such  facts,  for  the  purpose  of  ascertaining  their  character 
as  parts  of  a  given  whole.  When  we  have  satisfied  ourselves  on 
this  subject,  we  then  reason  from  the  parts  to  the  whole,  and 
we  reason  thus :  What  belongs  to  the  individuals  constituting 
'a  given  class  belongs  to  the  class  itself.  This  characteristic  be- 
longs to  such  individuals ;  it,  therefore,  belongs  to  the  class  itself. 
This  is  the  inductive  syllogism.  When  this  process  is  com- 
pleted we  then  reverse  it,  and  reason  from  the  whole  to  its  con- 
stituent parts,  thus :  All  of  this  class  have  this  characteristic ; 
A  belongs  to  tliis  class ;  therefore  he  has  this  characteristic. 
This  is  the  deductive  syllogism.  The  two  have  a  fixed  relation 
to  each  other,  the  latter  always  presupposing  and  depending 
for  its  validity  upon  the  former. 

In  adducing  individual  facts  in  a  process  of  investigation,  we 
do  not  even  then  conclude  from  the  particular  to  the  general, 
but  from  individuals  to  individuals.  One  individual,  for  exam- 
ple, in  a  course  of  experiments  upon  a  mass  of  matter  called 
gold  discovers  some  new  property  in  it.  The  mass  before  him* 
he  calls  gold,  because  it  presents  all  the  elements  of  the  concep- 
tion represented  by  the  term  under  consideration.  When  the 
new  fact  appears,  his  first  and  great  inquiry  is,  Whether  it  arises 
from. the  essential  properties  of  the  substance  itself,  or  from 
some  foreign  substance  accidentally  connected  with  it  ?  When 
this  question  is  resolved  and  the  new  fact  is  found  to  be  the  re- 
sult of  the  essential  elements  of  this  substance,  it  is  assumed  as 
itself  an  essential  element  of  our  conception  of  this  substance. 
On  what  groimds  ?  Because  we.  have  reasoned  from  the  indi- 
vidual to  the  class  ?  By  no  means ;  but  because  it,  with  the 
other  elements  referred  to,  now  enters  into  our  fundamental 
conceptions  of  the  substance  itself,  and  no  individual  mass  want- 
ing this  characteristic  can  take  rank  under  this  conception.  If 
it  should  be  found  that  this  fact  characterized  some  masses  and 
not  others  reckoned  as  gold,  this  would  occasion  a  separation  of 
such  masses  into  ,two  species,  one  having,  and  the  other  not  hav- 
ing, this  characteristic.  When  we  have  formed  a  general  con- 
ception, an  individual  to  take  rank  under  it,  must  represent  all 
the  elements  included  in  the  conception.     The  conception  does 


ANALYTIC      OF      SYLLOGISMS.  181 

not  represent  a  mass  of  individuals  whose  character  we  do  not 
know,  and  in  respect  to  each  of  whom,  without  having  obtained 
such  knowledge,  we  reason  from  the  general  conception.  On 
the  other  hand,  it  represents  a  class  which  we  do  know,  and 
from  which,  consequently,  we  reason  to  said  individuals.  We 
first  know  the  individuals,  and  from  the  elements  common  to 
them  all  abstracted,  we  form  the  general  conception,  and  when 
we  reason  back  from  the  conception  to  the  individuals,  Ave  do 
not  reason  from  the  known  to  the  unknown,  but  from  the 
known  to  the  known.  I  would  here  invite  very  special  atten- 
tion to  the  following  lengthy  extract  from  Sir  William  Hamil- 
ton, as  presenting  all  that  need  be  added  upon  this  subject : 

"  Logic  does  not  consider  things  as  they  exist  really  and  in 
themselves,  but  only  the  general  forms  of  thought  under  which 
the  mind  conceives  them  ;  in  the  language  of  the  schools,  logic 
is  conversant,  not  about  first,  but  about  second,  notions.  Thus 
a  logical  inference  is  not  determined  by  any  objective  relation 
of  causality  subsisting  between  the  terms  of  the  premises  and 
conclusion,  but  solely  by  the  subjective  relation  of  reason  and 
consequent  under  which  they  are  construed  to  the  mind  in 
thought.  The  notion  conceived  as  determining  is  the  reason  ; 
the  notion  conceived  as  determined  is  the  consequent ;  and  the 
relation  between  the  two  is  the  consequence.  Now,  the  mind 
can  think  two  notions  under  the  formal  relation  of  consequence 
only  in  one  or  other  of  tAvo  modes.  Either  the  determining 
notion  must  be  conceived  as  a  whole,  containing  (under  it), 
and,  therefore,  necessitating  the  determined  notion  conceived 
as  its  contained  part  or  parts  ;  or,  the  determining  notion  must 
be  conceived  as  the  parts  constituting,  and,  therefore,  necessi- 
tating the  determined  notion  conceived  as  their  constituted 
whole.  Considered,  indeed,  absolutely  and  in  themselves,  the 
whole  and  all  the  parts  are  identical.  Relatively,  however,  to 
us  they  are  not,  for  in  the  order  of  thought  (and  logic  is  only 
conversant  with  the  laAvs  of  thought),  the  whole  may  be  con- 
ceived first,  and  then,  by  mental  analysis,  separated  into  its 
parts  ;  or,  the  parts  may  be  conceived  first,  and  then,  by  men- 
tal synthesis,  collected  into  a  Avhole.     Logical  inference  is  thus 


182  LOGIC. 

of  two,  and  only  of  two,  kinds ;  it  must  proceed,  either  from  the 
whole  to  the  parts,  or  from  the  parts  to  the  whole ;  and  it  is 
only  under  the  character  of  a  constituted  or  containing  whole, 
or,  of  a  constituting  or  contained  part,  that  any  thing  can  he- 
come  the  term  of  a  logical  argumentation. 

Before  proceeding  we  must,  however,  allude  to  the  nature  of 
the  whole  and  part,  ahout  which  logic  is  conversant.  These 
are  not  real  or  essential  existences,  hut  creations  of  the  mind 
itself  in  secondary  operation  on  the  primary  ohjects  of  its  know- 
ledge. Things  may  be  conceived  the  same,  inasmuch  as  they 
are  conceived  the  street  of  the  same  attribute  or  collection  of 
attributes  (i.  e.  of  the  same  nature)  ;  inasmuch  as  they  are  con- 
ceived the  same,  they  must  be  conceived  as  the  parts  constituent 
of,  and  contained  under,  a  whole ;  and  as  they  are  conceived 
the  same  only  as  they  are  conceived  to  be  the  subject  of  the 
same  nature,  this  common  nature  must  be  convertible  with  that 
ichole.  A  logical  or  universal  whole  is  called  a  genus  when  its 
parts  are  thought  as  also  containing  wholes  or  species ;  a  spe- 
cies when  its  parts  are  thought  as  only  contained  parts  or  indi- 
viduals. Genus  and  species  are  each  called  a  class.  Except 
the  highest  and  the  lowest,  the  same  class  may  thus  be  thought 
either  as  a  genus  or  as  a  species. 

Such  being  the  nature  and  relations  of  a  logical  whole  and 
parts,  it  is  manifest  what  must  be  the  conditions  under  which 
the  two  kinds  of  logical  inference  are  possible.  The  one  of 
these,  the  process  from  the  whole  to  the  parts,  is  deductive  rea- 
soning (or  syllogism  proper)  ;  the  other,  the  process  from  the 
parts  to  the  whole,  is  inductive  reasoning.  The  former  is  gov- 
erned by  the  rule :  What  belongs  {or  does  not  belong)  to  the 
containing  whole,  belongs  {or  does  not  belong)  to  each  and  all 
of  the  contained  parts.  The  latter  by  the  rule  :  What  belongs 
{or  does  not  belong)  to  all  the  constituent  parts,  belongs  {or  does 
not  belong)  to  the  constituted  whole.  These  rules  exclusively 
determine  all  formal  inference  ;  whatever  transcends  or  vio- 
lates them,  transcends  or  violates  logic.  Both  are  equally  abso- 
lute. It  would  be  not  less  illogical  to  infer  by  the  deductive 
syllogism,  an  attribute  belonging  to  the  whole  of  something  it 


ANALYTIC      OF     SYLLOGISMS.  183 

was  not  conceived  to  contain  as  a  part,  than  by  the  inductive, 
to  conclude  of  the  whole  what  is  not  conceived  as  a  predicate 
of  all  its  constituent  parts.  In  either  case  the  consequent  is  not 
thought  as  determined  by  the  antecedent ;  the  premises  do  not 
involve  the  conclusion. 

The  deductive  and  inductive  processes  are  elements  of  logic 
equally  essential.  Each  requires  the  other.  The  former  is  only 
possible  through  the  latter  ;  and  the  latter  is  only  valuable  as 
realizing  the  possibility  of  the  former.  As  our  knowledge  com- 
mences with  the  apprehension  of  singulars,  every  class  or  uni- 
versal whole  is  consequently  only  knowledge  at  second-hand. 
Deductive  reasoning  is  tlms  not  an  original  and  independent 
process.  The  universal  major  proposition,  out  of  which  it  de- 
velops the  conclusion,  is  itself  necessarily  the  conclusion  of  a 
foregone  induction,  and,  mediately  or  immediately,  an  infer- 
ence;  a  collection  from  individual  objects  of  perception  or  self- 
consciousness.  Logic,  therefore,  as  a  definite  and  sell-sufficient 
science,  must  equally  vindicate  the  formal  purity  of  the  ana- 
lytic illation  by  which  it  ascends  to  its  wholes,  as  of  the  syn- 
thetic illation  by  which  it  re-descends  to  their  parts." 


Section  IX. — Syllogisms  of  Induction  and  Analogy. 

Demonstrative,  inductive,  and   analogical  reasoning  distin- 
guished. 

There  are  three  kinds  of  conclusions  deduced  from  different 
kinds  of  premises  :  what  is  commonly  called  the  demonstrative, 
in  which,  in  general,  we  obtain  necessary  truths,  truths  whose 
opposites  are  inconceivable  and  impossible  ;  truths  of  induction, 
truths  which  are  real,  but  whose  opposites  are  conceivable,  and 
therefore,  in  themselves,  possible ;  and  deductions  of  analogy, 
deductions  based  upon  such  remote  relations  as  to  claim  our 
regard  only  as  probably  true.  Syllogisms  which  yield  the  first 
class  of  truths  are  denominated  by  Kant,  and  with  perfect  pro- 
priety, "  syllogisms  of  reason."  Those  which  yield  the  last  two 
kinds  of  conclusions  he  calls  syllogisms  of  the  understanding,  this 


latter  class  being  divided  into  two  species,  those  of  induction 
and  those  of  analogy.  The  distinction  between  syllogisms  of 
reason  and  of  the  understanding  is  perfectly  obvious.  To  the 
former  pertain  all  mathematical  truths  and  those  of  a  kindred 
nature.  To  the  latter  belong  all  truths  in  respect  to  matters 
of  fact,  and  deductions  from  the  same  relative  to  the  universe 
of  matter  and  spirit.  The  distinction  between  arguments  of  in- 
duction and  analogy,  however,  is  not  so  obvious,  excepting  in 
their  extreme  relations.  Perhaps  the  following  statements  will 
render  this  distinction  as  clear  and  distinct,  as  is  practicable 
from  the  point  of  observation  from  which  the  subject  is  gen- 
erally viewed.  When  facts  are  adduced  which  can  be  really  or 
professedly  explained,  but  upon  a  given  hypothesis  relative  to 
the  cause  or  law  of  their  occurrence,  and  when  the  object  for 
which  said  facts  are  adduced  is  to  establish  such  hypothesis,  the 
reasoning  is  inductive.  On  the  other  hand,  .suppose  that  in 
connection  with  a  certain  object  A,  we  find  certain  qualities 
X  Y  Z  and  also  M,  while  no  causal  connection  is  perceived  be- 
tween M  and  the  other  qualities  named.  All  that  is  given  is 
the  fact  of  coexistence  in  this  case.  In  another  object  B,  we 
perceive  the  qualities  X  Y  Z,  and  are  not  able  from  our  rela- 
tions to  B  to  determine  immediately  whether  it  has  also  the 
quality  M  or  not.  From  the  fact  that  this  characteristic  is 
found  connected  with  X  Y  Z  in  A,  we  conclude  that  it  exists, 
also,  in  connection  with  the  same  qualities  in  B.  In  this  case 
our  reasoning  is  wholly  analogical.  In  analogical  reasoning  we 
infer  from  the  fact  of  coexistence  in  one  case  mere  coexistence 
in  another.  In  induction  we  argue,  from  certain  facts  of  coex- 
istence, the  relation  of  cause  and  effect,,  or  of  law,  &c,  in  all 
cases  of  the  same  kind.  An  inductive  inference  is  valid  when 
all  the  facts  can  be  explained  by  the  hypothesis  presented,  and 
by  no  other  conceivable  one,  and  each  inference  has  greater  or 
less  claims  to  validity  according  to  its  relations  to  this  one  prin- 
ciple. An  argument  from  analogy  to  have  force  must  possess 
the  following  characteristics:  1.  The  quality  M  must  not  be 
known  to  be  connected  with  X  Y  Z,  nor  to  be  unconnected 
with  them.     If  M  were  shown  to  be  the  result  of  some  cause  in 


ANALYTIC      OF     SYLLOGISMS.  185 

A  which  has  no  connection  with  X  Y  Z,  then  the  argument  is 
vi.  no  force  at  all.  2.  It  must  be  seen  that  the  relation  of  ante- 
cedence and  consequence  of  some  kind  may  exist  between  them, 
a  relation  followed  by  that  of  uniform  coexistence.  3.  .The 
characteristics  must  be  so  related  to  each  other  as  to  favor  the 
supposition  of  such  a  relation.  4.  This  supposition  must  not  be 
overbalanced  by  stronger  facts  of  an  opposite  nature.  When 
all  these  circumstances  combine  in  the  same  case,  they  present 
a  very  strong  argument  from  analogy. 

When  Sir  Isaac  Newton,  for  example,  adduced  facts  to  prove 
the  principle  or  law,  that  all  bodies  attract  each  other  in  pro- 
portion directly  as  the  amount  of  matter  which  they  contain, 
and  inversely  as  the  squares  of  their  mean  distance,  his  argu- 
ment was  inductive.  When,  on  the  other  hand,  from  having 
observed  that  objects  which  are  combustible  have  the  power  of 
refracting  light,  .he  inferred  that  the  diamond  and  water  are 
both  combustible,  because  both  alike  possess  the  refracting 
power  in  proportion  to  their  density,  he  reasoned  from  analogy. 
The  following  extract  from  "Mills'  Logic"  presents  another 
illustration  of  this  form  of  argument : 

"  For  example,  I  might  infer  that  there  are  probably  inhabi- 
tants in  the  moon,  because  there  are  inhabitants  on  the  earth, 
in  the  sea,  and  in  the  air,  and  this  is  the  evidence  of  analogy. 
The  circumstance  of  having  inhabitants  is  here  assumed  not  to 
be  an  ultimate  property,  but  (as  it  is  reasonable  to  suppose)  a 
consequence  of  other  properties ;  and  depending,  therefore,  in 
the  case  of  our  earth,  upon  some  of  its  properties  as  a  portion 
of  the  universe,  but  upon  which  of  those  properties  we  know 
not.  Now,  the  moon  resembles  the  earth  in  being  a  solid,  . 
opaque,  nearly  spherical  substance ;  containing  active  volca- 
noes ;  receiving  heat  and  light  from  the  sun  in  about  the  same 
quantity  as  our  earth ;  revolving  on  its  axis,  whose  materials 
gravitate,  and  which  obey  all  the  various  laws  resulting  from 
that  property.  And  I  think  no  one  will  deny  that  if  this  were 
all  that  was  known  of  the  moon,  the  existence  of  inhabitants  in 
that  luminary  would  derive  from  these  various  resemblances  to 
the  earth,  a  greater  degree  of  probability  than  it  would  other- 


wise  have,  although  the  amount  of  the  augmentation  it  would 
be  ridiculous  to  attempt  to  estimate. 

"  If,  however,  every  resemblance  proved  between  B  and  A,  in 
any  point  not  known  to  be  immaterial  with  respect  to  M,  forms 
some  additional  reason  for  presuming  that  B  has  the  attribute 
M,  it  is  clear,  £  contra,  that  every  dissimilarity  which  can  be 
proved  between  them  furnishes  a  counter-probability  of  the 
same  nature  on  the  other  side.  It  is  not,  hideed,  impossible 
that  different  ultimate  properties  may,  in  some  particular  in- 
stances, produce  the  same  derivative  property ;  but  on  the 
whole  it  is  certain  that  things  which  differ  in  their  ultimate 
properties,  will  differ  at  least  as  much  in  the  aggregate  of  their 
derivative  properties,  and  that  the  differences  which  are  un- 
known will  on  the  average  of  cases  bear  some  proportion  to 
those  which  are  known.  There  will,  therefore,  be  a  competi- 
tion between  the  known  points  of  agreement  and  the  known 
points  of  difference  in  A  and  B  ;  and  according  as  the  one  or 
the  other  are  deemed  to  preponderate,  the  probability  derived 
from  analogy  will  be  for  or  against  B's  having  the  property  M. 
The  moon,  for  instance,  agrees  with  the  earth  in  the  circum- 
stances already  mentioned  ;  but  differs  in  being  smaller,  in  hav- 
ing its  surface  more  unequal,  and  apparently  volcanic  through- 
out ;  having  no  atmosphere  sufficient  to  refract  light ;  no  clouds, 
therefore  (it  is  inferentially  concluded)  no  water.  These  differ- 
ences, considered  merely  as  such,  might  perhaps  balance  the  re- 
semblances, so  that  analogy  would  afford  no  presumption  either 
way.  But  considering  that  some  of  the  circumstances  which 
are  wanting  on  the  moon  are  among  those  which,  on  our  earth, 
are  found  to  be  indispensable  conditions  of  animal  life,  we  may 
conclude  that  if  that  phenomenon  does  exist  in  the  moon,  it 
must  be  as  the  effect  of  causes  totally  different  from  those  on 
which  it  depends  here ;  as  a  consequence,  therefore,  of  the 
moon's  differences  from  the  earth,  not  of  their  points  of  agree- 
ment. Viewed  in  this  light,  all  the  resemblances  Avhich  exist 
become  presumptions  against,  or  in  favor  of,  her  being  inhabit- 
ed. Since  life  cannot  exist  there  in  the  manner  in  which  it 
exists  here,  the  greater  the  resemblance  of  the  lunar  world  to 


ANALYTIC      OF     SYLLOGISMS.  187 

the  terrestrial  in  all  other  respects,  the  less  reason  we  have  to 
believe  that  it  can  contain  life." 

Canon  of  the  Inductive  Syllogism. 

The  canon  of  the  inductive  syllogism  is  this :  When  many- 
facts  of  a  given  class  have  common  essential  characteristics,  this 
resemblance  arises  from  a  common  ground  or  cause,  and  that 
hypothesis  which  not  only  accords  with  the  facts,  but  alone  ex- 
plains them  all,  must  be  assumed  as  such  ground. 

General  characteristics  of  all  facts  ov  principles  which  are  to 
be  assumed  as  causes  or  laws. 

The  following  lengthy  extract  from  "Thomson's  Laws  of 
Thought,"  contains  the  tests  laid  down  by  Sir  John  Herschel 
of  all  tacts  and  principles  of  this  kind.  To  this  is  added,  from 
the  same  author,  an  account  of  some  important  experiments  in 
natural  science ;  experiments  made  by  Sir  Humphrey  Davy. 
We  give  these  experiments  in  illustration  of  the  general  pro- 
cess of  induction  in  the  natural  sciences  : 

"  In  order  to  constitute  any  tact  or  principle  the  cause  of 
other  facts,  it  should  possess  the  following  characters  :  * 

A.  '  Invariable  connection,  and,  in  particular,  invariable  an- 
tecedence of  the  cause  and  consequence  of  the  effect,  unless 
prevented  by  some  counteracting  cause.' 

B.  'Invariable  negation  of  the  effect  with  absence  of  the 
cause,  unless  some  other  cause  be  capable  of  producing  the 
same  effect.'  The  application  of  this  principle  has  been  called 
the  Method  of  Difference. 

C.  'Increase  or  diminution  of  the  effect,  with  the  increased 
or  diminished  intensity  of  the  cause,  in  cases  which  admit  of 
increase  and  diminution.' 

D.  '  Proportionality  of  the  effect  to  its  cause  in  all  cases  of 
direct  unimpeded  action.' 

E.  '  Reversal  of  the  effect  with  that  of  the  cause.'     The  ap- 

*  Sir  John  HerschePs  Preliminary  Discourse,  p.  151. 


188  LOGIC. 

plication  of  the  three  last  principles  constitutes  the  Method  of 
Concomitant  Variations. 

From  these  principles  follow  some  practical  rules  for  ascer- 
taining causes ;  such  as : 

1.  The  cause  of  a  given  effect  may  be  the  same  as  we  know 
to  produce  some  similar  effect  in  another  case  better  known 
to  us. 

,  For  example,  Berzelius  records  that  a  small  bubble  of  the 
gas  called  seleniuretted  hydrogen,  inspired  by  accident  through 
the  nose,  deprived  him  for  some  hours  of  the  sense  of  smell,  and 
left  a  severe  catarrh  which  lasted  for  fifteen  days.  Dr.  Prout 
suggests  that  the  corresponding  effects  in  influenza  may  be 
traceable  to  the  same  cause  as  undoubtedly  produced  them 
here,  to  the  admixture,  namely,  of  this  or  some  similar  sub- 
stance with  the  air  we  breathe  ;  and  as  a  suggestion  or  antici- 
pation this  is  perfectly  legitimate,  and  may  prove  highly  valua- 
ble. Its  inadequacy  as  a  proof  may  be  shown  by  throwing  it 
into  syllogistic  form  : 

The  case  of  inspiring  seleniuretted  hydrogen  is  a  case  in  which  loss  of  smell 

and  severe  catarrh  follow  ; 
Cases  of  influenza  exhibit  these  effects  ; 
Therefore,  cases  of  influenza  are  cases  in  which  the  said  gas  has  been  inspired. 

This  is  the  mood  AAA,  Fig.  II.,  invalid  because  it  does  not 
distribute  the  middle  term. 

2.  'If  in  any  of  the  facts  we  have  to  account  for,  there  be 
even  one  in  which  a  particular  character  is  wanting,  that  char- 
acter cannot  be  the  cause  in  question ;  for  the  true  cause  can 
never  be  absent.' 

3.  'As  the  laws  of  nature  are  uniform,  and  never  capricious, 
we  are  entitled  to  expect  that  a  cause  which  in  several  cases 
produces  a  given  effect  will  always  do  so  ;  and  if  it  appeal's  to 
be  otherwise,  we  should  either  search  for  some  counteracting 
causes,  or  suspect  the  accuracy  of  our  observations.' 

4.  '  Causes  will  very  frequently  become  obvious  by  a  mere 
arrangement  of  our  facts  in  the  order  of  intensity  in  which 
some  peculiar  quality  subsists ;  though  not  of  necessity,  because 


ANALYTIC     OF     SYLLOGISMS.  189 

counteracting  or  modifying  causes  may  be  at  the  same  time  in 
action.' 

'  For  example,  sound  consists  in  impulses  communicated  to 
our  ear  by  the  air.  If  a  series  of  impulses  of  equal  force  be 
oommunicated  to  it  at  equal  intervals  of  time,  at  first  in  slow 
succession,  and  by  degrees  more  and  more  rapidly,  we  hear  at 
first  a  rattling  noise,  then  a  low  murmur,  and  then  a  hum, 
which  by  degrees  acquires  the  character  of  a  musical  note, 
rising  higher  and  higher  in  acuteness,  till  its  pitch  becomes  too 
high  for  the  ear  to  follow.  And  from  this  correspondence  be- 
tween the  pitch  of  the  note  and  the  rapidity  of  succession  of  the 
impulse,  we  conclude  that  our  sensation  of  the  different  pitches 
of  musical  notes  originates  in  the  different  rapidities  with 
which  these  impulses  are  communicated  to  our  ears.'  To  make 
such  an  arrangement,  however,  we  must  have  a  presage,  and 
no  uncertain  one,  of  the  cause  of  our  phenomena ;  and,  there- 
fore, it  is  rather  useful  for  verification,  than  for  suggestion,  of  a 
theory. 

5.  'If  we  can  either  find  produced  by  nature,  or  produce  de- 
signedly for  ourselves,  two  instances  which  agree  exactly  in  all 
but  one  particular,  and  differ  in  that  one,  its  influence  in  pro- 
ducing the  phenomenon,  if  it  have  any,  must  thereby  be  ren- 
dered sensible.  If  that  particular  be  present  in  one  instance, 
and  wanting  altogether  in  the  other,  the  production  or  non- 
production  of  the  phenomenon  will  decide  whether  it  be  or  be 
not  the  only  cause  ;  still  more  evidently,  if  it  be  present  contra- 
riwise in  the  two  cases,  and  the  effect  be  thereby  reversed.  But 
if  its  total  presence  or  absence  only  produces  a  change  in  the 
degree  or  intensity  of  the  phenomenon,  we  can  then  only  con- 
clude that  it  acts  as  a  concurrent  cause  or  condition  with  some 
other  to  be  sought  elsewhere.  In  nature,  it  is  comparatively 
rare  to  find  instances  pointedly  differing  in  one  circumstance 
and  agreeing  in  every  other ;  but  when  we  call  experiment  to 
our  aid,  it  is  easy  to  produce  them ;  and  this  is,  in  fact,  the 
grand  application  of  experiments  of  inquiry  in  physical  re- 
searches. They  become  more  valuable,  and  their  results 
clearer,  in  proportion  as  they  possess  this  quality  (of  agreeing 


190  LOGIC. 

exactly  in  all  their  circumstances  but  one),  since  the  question 
put  to  nature  becomes  thereby  more  pointed,  and  its  answer 
more  decisive.' 

6.  '  Complicated  phenomena,  in  which  several  causes  concur- 
ring, opposing,  or  quite  independent  of  each  other,  operate  at 
once,  so  as  to  produce  a  compound  effect,  may  be  simplified 
by  subducting  the  effect  of  all  the  known  causes,  as  well  as 
the  nature  of  the  case  permits,  either  by  deductive  reasoning 
or  by  appeal  to  experience,  and  thus  leaving,  as  it  were,  a 
residual  phenomenon  to  be  explained.  It  is  by  this  process, 
in  fact,  that  science,  in  its  present  advanced  state,  is  chiefly 
promoted.' 

'  A  very  elegant  example  may  be  cited,  from  the  explanation 
of  the  phenomena  of  sound.  The  inquiry  into  the  cause  of 
sound  had  led  to  conclusions  respecting  its  mode  of  propaga 
tion,  from  which  its  velocity  in  the  air  could  be  precisely  calcu- 
lated. The  calculations  were  performed ;  but,  when  compared 
with  fact,  though  the  agreement  was  quite  sufficient  to  show 
the  general  correctness  of  the  cause  and  mode  of  propagation 
assigned,  yet  the  whole  velocity  could  not  be  shown  to  arise 
from  this  theory.  There  was  still  a  residual  velocity  to  be  ac- 
counted for.  At  length  La  Place  struck  on  the  happy  idea, 
that  this  might  arise  from  the  heat  developed  in  the  act  of  that 
condensation  which  necessarily  takes  place  at  every  vibration 
by  which  sound  is  conveyed.  The  matter  was  subjected  to 
exact  calculation,  and  the  result  was  at  once  the  complete  ex- 
planation of  the  residual  phenomenon.' 

These  are  specimens  of  the  methods  according  to  which  re- 
searches into  causes  are  conducted.  I  add  one  example,  com- 
bining the  4th,  5th,  and  6th  rules,  and  exhibiting  Proportionali- 
ty of  cause  and  effect,  Experiment,  and  Residual  Phenomena 
in  one  set  of  inquiries.  Beyond  this,  the  limits  I  have  pre- 
scribed myself  do  not  suffer  mc  to  go. 

In  Sir  Humphrey  Davy's  experiments  upon  the  decomposi- 
tion of  water  by  galvanism,  it  was  found  that,  besides  the  two 
components  of  water,  oxygen  and  hydrogen,  an  acid  and  an 
alkali  were  developed  at  the  two  opposite  poles  of  the  machine. 


ANALYTIC     OF     SYLLOGISMS.  191 

As  the  theory  of  the  analysis  of  water  did  not  give  reason  to 
expect  these  products,  they  were  a  residual  phenomenon,  the 
cause  of  which  was  still  to  be  found.  Some  chemists  thought 
that  electricity  had  the  power  of  producing  these  substances  of 
itself;  and  if  their  erroneous  conjecture  had  been  adopted,  suc- 
ceeding researches  would  have  gone  upon  a  false  scent,  consid- 
ering galvanic  electricity  as  a  producing  rather  than  a  decom- 
posing force.  The  happier  insight  of  Davy  conjectured  that 
there  might  be  some  hidden  cause  of  this  portion  of  the  effect ; 
the  glass  vessel  containing  the  water  might  suffer  partial  <le- 
composition,  or  some  foreign  matter  might  be  mingled  with  the 
water,  and  the  acid  and  alkali  be  disengaged  from  it,  so  that 
the  water  would  have  no  "share  in  their  production.  Assuming 
this,  he  proceeded  to  try  whether  the  total  removal  of  the  camse 
(B.  p.  187)  would  destroy  the  effect,  or  at  least  the  diminution 
of  it  cause  a  corresponding  change  in  the  amount  of  effect  pro- 
duced (C.  p.  187).  By  the  substitution  of  gold  vessels  for  the 
glass  without  any  change  in  the  effect,  he  at  once  determined 
that  the  glass  was  not  the  cause.  Employing  distilled  water, 
he  found  a  marked  diminution  of  the  quantity  of  acid  and  alkali 
evolved ;  still  there  was  enough  to  show  that  the  cause,  what- 
ever it  was,  was  still  in  operation.  Impurity  of  the  water  was 
not  the  sole,  but  a  concurrent  cause.  He  now  conceived  that 
the  perspiration  from  the  hands,  touching  the  instruments, 
might  affect  the  case,  as  it  would  contain  common  salt,  and  an 
acid  and  an  alkali  would  result  from  its  decomposition  under 
the  agency  of  electricity.  By  carefully  avoiding  such  contact, 
he  reduced  the  quantity  of  the  products  still  further,  until  no 
more  than  slight  traces  of  them  were  perceptible.  What  re 
mained  of  the  effect  might  be  traceable  to  impurities  of  the  at 
mosphere,  decomposed  by  contact  with  the  electrical  apj^aratus 
An  experiment  determined  this  ;  the  machine  was  placed  undei 
an  exhausted  receiver,  and  when  thus  secured  from  atmospheric 
influence,  it  no  longer  evolved  the  acid  and  the  alkali. 

A  formal  analysis  of  these  beautiful  experiments  will  illus- 
trate the  method  of  applying  the  rules  of  pure  logic  in  other 


192  LOGIC. 

I. — Statement  of  the  case,  the  residual  cause  being  still  undiscovered  : 

'  The  decomposition  of  water  by  electricity,  produces  oxygen  and 
hydrogen,  with  an  acid  and  an  alkali. ' 
II. — Separation  of  the  residual  from  the  principal  cause  : 

a.  '  The  decomposition  of  water  produces  oxygen  and  hydrogen.' 

b.  '  The  production  of  an  acid  and  alkali  in  the  decomposition  of 
water  may  be  caused  by  action  on  the  glass  vessel  containing  the 
water.' — (Problematical  judgment,  A.) 

HI. — The  latter  judgment  (b)  disproved  by  a  syllogism  in  mood  E  A  0, 
Fig.  III.,  with  a  conclusion  that  contradicts  it : 

'  A  case  in  which  I  employ  a  vessel  of  gold  cannot  involve  any  de- 
composing action  on  a  glass  vessel ;' 
'  A  case  in  which  I  employ  a  gold  vessel  still  gives  the  acid  and 

the  alkali ;' 
'  Therefore,  cases  of  the  production  of  the  acid  and  alkali  are  not 
always  cases  in  which  glass  is  decomposed.' 

IV. — Another  attempt  to  suggest  the  residual  cause  : 

'The  acid  and  alkali  are  produced  by  the  decomposition  of  impu- 
rities in  the  water  employed.'    . 

Syllogism  in  A  A  I,  Fig.  III.,  tending  to  prove  this. 

'  An  experiment  with  distilled  water  must  admit  less  impurity  ;' 

'An  experiment  with  distilled  water  gives  less  acid  and  alkali ;' 

'  Therefore,  sometimes  with  less  impurity  we  have  less  acid  and 
alkali.' 
V. — 'The  contact  of  moist  hands'  may  be  an  additional  cause  of  the  re- 
sidual phenomenon  : 

Improved  syllogism  in  A  A  I,  Fig.  III.,  to  include  this  concurrent 
cause. 

'An  experiment  with  distilled  water,  and  apparatus  kept  from 
contact  of  hands  will  admit  still  less  impurity  ;' 

'An  experiment,  &c,  results  in  the  production  of  still  less  acid 
and  alkali ;' 

'  Therefore,  sometimes  with  still  less  impurity  we  have  stiy.  less 
acid  and  alkali.' 
VI. — Amended  syllogism— A  A  A,  Fig.  Ill : 

'  A  case  where  we  use  these  precautions  in  vacuo  is  a  case  of  no  im- 
purity ;' 

'  A  case  where  we  use,  &c. ,  in  vacuo  is  a  case  of  no  acid  and  alkali ;' 

'  Therefore,  a  case  of  no  impurity  is  a  case  of  no  acid  and  alkali.' 
VII. — Immediate  inference  from  last  conclusion  : 

'Cases  of  no-impurity  are   cases  of  non-production  of  acid  and 


ANALYTIC     OF     SYLLOGISMS.  193 

'Therefore'  (according  to  the  example  in  p.  219,  Division  II.,  of 
inference  from  A), 

'  All  cases  of  production  of  acid  and  alkali  are  cases  of  some  impu- 
rity ;' 

which  was  to  he  proved. 

An  example  like  this  brings  into  a  strong  light  many  of  the 
characteristics  of  inductive  reasoning.  Forms  usually  consid- 
ered to  be  deductive  are  here  freely  employed.  The  later  steps 
tend  to  confirm  the  earlier,  on  which,  however,  they  themselves 
depend  ;  so  that  a  mutual  confirmation  is  obtained  from  setting 
them  together.  When  the  chemist  substituted  gold  vessels  for 
the  glass,  and  inferred  from  the  continuance  of  the  effect  under 
this  change  that  the  glass  could  have  nothing  to  do  with  its 
production,  it  was  formally  possible  in  the  then  state  of  know- 
ledge that  the  glass  might  be  the  cause  in  the  one  experiment, 
and  the  decomposition  of  the  gold  in  the  other.  But  the  later 
steps,  which  showed  that  the  effect  varied  with  the  variations 
in  a  circumstance  wholly  distinct  from  the  decomposition  of 
glass  or  gold,  reduced  the  possibility  of  maintaining  such  a 
view  to  the  very  lowest  amount.  Even  the  premises  of  par- 
ticular syllogisms  in  the  chain  are  sometimes  tested  and  cor- 
rected by  the  conclusion,  although  formally  the  conclusion 
should  entirely  depend  upon  the  premises.  The  experimenter 
expected  to  find  that  the  use  of  distilled  water  would  exclude 
all  impurity ;  and  he  intended  that  his  premise  (see  No.  IV.) 
should  assert  as  much  ;  but  when  it  turned  out  in  the  conclu- 
sion that  the  supposed  products  of  the  impurity  were  still 
present,  he  was  reduced  to  the  choice  between  abandoning 
that  cause  and  re-casting  his  premise  so  as  to  admit  that  the 
cause  was  still  present :  '  the  use  of  distilled  water  gives  less 
impurity.' " 

VERIFICATION    OF    INDUCTIONS. 

When  such  inductions  have  been  made  we  may  wish  to  veri- 
fy them.     On  this  topic  we  are  also  indebted  to  Mr.  Thomson 
for  the  following  extract  from  the  "  Quarterly  Review,"  an  ex- 
tract upon  which  our  author  remarks  :  "  I  transcribe  this  from 
9 


the  Quarterly  Review ;  as  I  despair  of  expressing  its  purport 
in  words  of  mine,  half  so  clearly  and  elegantly."  For  similar 
reasons  relative  to  ourselves,  we  give  the  extract  as  it  is  : 

"  Verification  of  Inductions. 

"  It  is  of  great  moment  to  distinguish  the  characters  of  a 
sound  induction.  One  of  them  is  its  ready  identification  with 
our  conception  of  facts,  so  as  to  make  itself  a  part  of  them,  to 
engraft  itself  into  language,  and  by  no  subsequent  effort  of  the 
mind  to  be  got  rid  of.  The  leading  term  of  a  true  theory  once 
pronounced,  we  cannot  fall  back  even  in  thought  to  that  help- 
less state  of  doubt  and  bewilderment  in  which  we  gazed  on  the 
facts  before.  The  general  proposition  is  more  than  a  sum  of 
the  particulars.  Our  dots  are  filled  in  and  connected  by  an 
ideal  outline  which  we  pursue  even  beyond  their  limits, — assign 
it  a  name,  and  speak  of  it  as  a  thing.  In  all  our  propositions 
this  new  thing  is  referred  to,  the  elements  of  which  it  is  formed 
forgotten  ;  and  thus  we  arrive  at  an  inductive  formula,  a  gen- 
eral, perhaps  a  universal,  proposition. 

"  Another  character  of  sound  inductions  is  that  they  enable 
us  to  predict.  We  feel  secure  that  our  rule  is  based  upon  the 
realities  of  nature,  when  it  stands  us  in  the  stead  of  more  expe- 
rience ;  when  it  embodies  facts,  as  an  experience  wider  than 
our  own  would  do,  and  in  a  way  that  our  ordinary  experience 
would  never  reach  ;  when  it  will  bear,  not  stress,  but  torture, 
and  gives  true  results  in  cases  studiously  different  from  those 
which  led  to  its  discovery.  The  theories  of  Newton  and  Fres- 
nel  are  full  of  such  cases.  In  the  latter,  indeed  [the  theory  of 
polarization],  this  test  is  carried  to  such  an  extreme,  that  theory 
has  actually  remanded  back  experiment  to  read  her  lesson  anew,  . 
and  convicted  her  of  blindness  and  error.  It  has  informed  her 
of  facts  so  strange  as  to  appear  to  her  impossible,  and  showed 
her  all  the  singularities  she  would  observe  in  critical  cases  she 
never  dreamed  of  trying. 

"  Another  character  which  is  exemplified  only  in  the  greatest 
theories,  is  the  consilience  of  inductions,  where  many  and  wide- 


ANALYTIC     OF     SYLLOGISMS.  195 

ly  different  lines  of  experience  spring  together  into  one  theory 
which  explains  them  all,  and  that  in  a  more  simple  manner  than 
seemed  to  be  required  for  either  separately.  Thus  in  the  infi- 
nitely varied  phenomenon  of  physical  astronomy,  when  all  are 
discussed  and  all  explained,  wTe  hear  from  all  quarters  the  con- 
sentaneous echoes  of  but  one  word,  '  gravitation.'  And  so  in 
optics  ;  each  of  its  endless  classes  of  complex  and  splendid  phe- 
nomena being  interpreted  by  its  own  conception  ;  when  these 
conceptions  are  assembled  and  compared,  they  all  turn  out  to 
be  translated  into  their  peculiar  language  of  the  single  phrase, 
'  transverse  undulation.'  Mr.  Whewill  has  given  us,  as  exam- 
ples of  the  logic  of  induction,  what  he  terms  deductive  tables 
of  each  of  these  noble  generalizations  which  enable  us  to  trace, 
as  in  a  map,  the  separate  rills  of  discovery  flowing  at  first 
each  in  its  OAvn  narrow  basin,  thence  confluent  into  important 
streams,  which,  uniting  into  one  grand  liver,  bear  downwards 
to  an  ocean  of  truth  beyond  our  tracing." 

CANON    OF   THE   SYLLOGISM     OF     ANALOGY. 

There  are  two  classes  of  objects  to  Avhich  the  argument  from 
analogy  is  applied,  to  wit,  similarity  of  ratios  or  relations  •  and 
similarity  of  attributes.  Mandeville,  for  example,  uses  this  ar- 
gument against  popular  education,  that,  "  If  the  horse  knew 
enough  he  would  throw  his  rider,"  intending  thereby  to  imply 
two  pairs  of  related  terms,  to  wit,  "As  the  horse  is  to  the 
rider,  so  is  the  people  to  its  rulers,"  and  to  assert  that,  since 
one  relation  depends  upon  the  continuance  of  ignorance  in  the 
horse,  the  other  depends  upon  the  continuance  of  ignorance 
among  the  people.  Here  is  an  argument  from  analogy  de- 
pending upon  assumed  similarity  of  relations.  The  argument, 
in  this  case,  is  fallacious,  because  no  such  similarity  exists. 
When,  on  the  other  hand,  it  is  argued  from  certain  similarity 
of  attributes,  that  the  moon  as  well  as  the  earth  is  inhabited, 
the  argument  is  based  upon  the  second  class  of  characteristics 
named  above.  The  argument  in  the  second  case  depends 
upon  the  principle  or  canon,  that  the  "  same  attributes  may  be 


V 


assigned  to  distinct,  but  similar  things,  provided  they  can  be 
shown  to  accompany  the  points  of  resemblance  in  the  things, 
and  not  the  points  of  difference."  The  argument  in  the  first 
case  rests  on  this  principle,  to  wit :  "  When  any  thing  resem- 
bles another  in  known  particulars,  it  will  resemble  it  in  the  un- 
known." "  They  must  not,"  in  the  language  of  Mr.  Thomson, 
"  be  of  the  same  kind,  but  only  of  a  similar  one ;  otherwise  the 
argument  is  a  mere  case  of  example.  Neither  must  the  usual 
tests  be  applied  to  prove  that  the  known  particulars  invariably 
accompany  the  unknown,  otherwise,  as  Mr.  Mills  observes, 
we  trench  upon  the  ground  of  induction.  In  venturing  thus  to 
assign  attributes  to  a  thing,  because  other  things  of  a  different 
class  have  them,  we  show  our  dependence  upon  the  regularity 
and  consistency  of  creation." 

The  above  remarks  are  sufficient  to  elucidate  the  distinction 
between  the  argument  from  induction  and  .analogy,  and  to  pre- 
sent a  distinct  view  of  the  object  of  our  investigations. 

When  the  Syllogism  of  Analogy  has  the  greatest  force. 

The  syllogism  of  analogy  has  the  greatest  force  when  em- 
ployed in  answering  objections  to  given  systems  of  truth. 
Suppose  that  it  is  urged,  that  a  certain  system  of  doctrine  can- 
not be  true,  because  a  certain  element  (M)  is  involved  in  it. 
In  reply,  it  is  shown,  that  M  does,  in  fact,  exist  in  connection 
with  another  system  which  must  be  admitted  to  be  true.  This 
reply,  if  valid,  totally  annihilates  the  objection  under  considera- 
tion. 

THE   ENTHYMEME. 

The  common  definition  of  the  enthymeme  is  this,  "  a  syllo- 
gism with  one  premise  suppressed,"  or,  more  properly,  "  a  syl- 
gjsm  with  but  one  premise  expressed."  Some  have  doubted 
the  correctness  of  this  definition.  Whether  the  form  of  the 
syllogism  here  defined  be  properly  called  the  enthymeme,  or 
not,  one  thing  is  certain,  that  it  requires  no  special  elucidation, 


ANALYTIC     OP     SYLLOGISMS.  197 

it  being  the  very  form  in  which,  in  ordinary  writing  and  speak- 
ing, all  kinds  of  argument  are  exp'ressed.  The  syllogism  mere- 
ly presents  what  is  really  implied  in  the  argument,  and  not 
what  is  always,  in  form,  expressed. 


Section  X. — The  Sokites,  ok  Chain  Syllogism. 
Term  defined. 

The  sorites  is  a  series  of  propositions  of  two  kinds  or  classes  : 

1.  That  in  which  the  predicate  of  the  first  proposition  is 
made  the  subject  of  the  second ;  and  so  on  till,  in  the  conclu- 
sion, the  predicate  of  the  last  proposition  is  affirmed  or  denied 
of  the  subject  of  the  first.     For  example : 

Every  A  is  B ; 

Every  B  is  C  ; 

Every  C  is  D  ; 

.-.  Every  A  is  D. 

2.  When  the  subject  of  the  first  is  made  the  predicate  of  the 
second,  and  so  on  till,  in  the  conclusion,  the  predicate  of  the 
first  premise  is  predicated  of  the  subject  of  the  last.  For 
example : 

Every  B  is  A ; 
Every  C  is  B  ; 
Every  D  is  C  ; 
Every  E  is  D  ; 
.-.  Every  E  is  A. 

It  is  self-evident,  that  each  of  the  above  processes  has  equal 
and  absolute  validity. 

Principles  on  which  this  Form  of  Reasoning  depends. 

The  following  are  the  principles  on  which  this  form  of  rea- 
soning depends : 

1.  When  the  terms  are  related  as  inferior  and  superior  con- 
ceptions, then  this  principle  for  affirmative  conclusions  obtains, 


to  wit :  Any  conception  ranks  under  (as  X  is  Z)  any  other  con- 
ception under  which  any  of.  its  (the  former's)  superior  concep- 
tions rank  ;  and,  for  negative  conclusions,  any  conception  disa- 
grees with  any  other  conception,  which  disagrees  with  any  of 
its  (the  former's)  superior  conceptions ;  and,  also,  with  any 
which  agree  with  any  conceptions  with  which  it  disagrees. 
We  will  illustrate  the  above  principles  by  a  few  examples. 

In  regard  to  affirmative  conclusions  we  need  only  refer  to 
the  two  examples  given  above.  In  the  first,  A  is  given  as  an 
inferior  conception,  ranking  under  B  as  its  superior ;  and  B,  as 
in  a  similar  manner,  included  under  C,  and  C  under  D,  and  D 
under  E.  E,  therefore,  in  the  line  of  extension,  stands  as  the 
superior  conception  of  A ;  as  such,  A  is  said  to  be  E.  In  the 
second  example,  A  is  given,  in  the  sense  explained,  as  superior 
to  B,  B  to  C,  C  to  D,  and  D  to  E.  To  each  alike,  therefore, 
A  sustains  the  relation  of  a  superior  conception,  and  the  propo- 
sition, "  Every  E  is  A,"  must  hold  as  logically  valid.  Let  us 
now  consider  examples  of  the  present  form  of  argument  yield- 
ing negative  conclusions : 

Every  A  is  B ;  Every  A  is  B  ; 

Every  B  is  C  ;  No  B  is  C  ; 

Every  C  is  D  ;  Every  D  is  C  ; 

No  D  is  E ;  Every  E  is  D  ; 

.-.  No  A  is  E.  .-.  No  A  is  E. 

In  the  first  example,  E  is  given  as  excluded  from  D,  which, 
as  a  superior  conception,  includes  A  as  its  inferior.  A,  then, 
must  be  excluded  from  E.  In  the  second  example,  E  is  given 
as  included  in  C,  which  is  wholly,  as  not  included  in  B,  ex- 
cluded from  A.  A,  therefore,  is  wholly  excluded  from  E,  and 
the  principles  above  stated  must  hold  universally. 

2.  When  the  terms  of  the  propositions  are  not  constituted  of 
inferior  and  superior  conceptions,  but  are  related  as  equal  or 
unequal,  &c,  then  the  principle  which  controls  all  deductions 
may  be  thus  stated :  Any  term  agreeing  with  a  given  term 
agrees  with  all  that  the  latter  does,  and  disagrees  with  all  that 
disagrees  with  it ;  and  when  a  term  disagrees  with  a  given 
term,  it  disagrees  with  all  that  agree  with  the  latter  term. 


ANALYTIC     OF     SYLLOGISMS.  199 

Thus,  if  A  agrees  with  B,  B  with  C,  C  with  D,  and  D  with  E, 
then  A  must  agree  with  E,  agreeing  as  the  former  does  with 
terms  which  agree  with  E.  If,  on  the  other  hand,  A  agrees 
with  B,  C,  and  D,  and  the  latter  disagrees  with  E,  A,  of 
course,  must  disagree  with  E.  On  the  other  hand  still,  if  A 
disagrees  with  B,  and  any  term  agrees  with  the  latter,  A,  of 
course,  disagrees  with  it. 

The  Sorites  can  have  but  one  particular,  and  one  negative, 
premise. 

From  the  nature  of  th^  sorites  it  is  manifest,  that  all  of  the 
premises,  the  first  excepted,  must  be  universal,  and  but  one  of 
them  negative.  If  we  should  say,  Some  A  is  B,  and  some  B 
is  C,  no  relation  coufd  from  hence  be  inferred  between  A  and 
C,  for  the  reason,  that  the  part  of  B  which  is  in  C  may  be  the 
part  of  the  former  which  does  not  contain  A.  So,  if  we  should 
say,  All  A  is  B  and  no  B  is  C,  and  no  C  is  D,  we  could  not 
from  hence  argue,  that  A  either  agrees  or  disagrees  with  D  ; 
and  that  because  D  is  given  as  disagreeing  with  some  thing 
which  disagrees  with  A,  and  which,  therefore,  from  aught  that 
appears  to  the  contrary,  may  either  agree  or  disagree  with  A. 

Forms  of  this  ki?id  of  argument. 

There  are  four  distinct  forms  of  the  argument  under  consid- 
eration : 

1.  When  all  the  premises  are  universal  affirmatives,  and  in 
the  conclusion  the  predicate  of  the  last  is  affirmed  of  the  sub- 
ject of  the  first :  All  A  is  D. 

2.  When  the  last  premise  is  negative,  and  in  the  conclusion 
the  subject  of  the  first  is  denied  of  the  predicate  of  the  last;  as, 
No  A  is  D.  If  the  first  premise  was  particular,  such  also  would 
be  the  conclusion,  to  wit :  Some  A  is  not  D. 

3.  When  the  first  premise  is  negative,  and  each  successive 
conception  is  given  as  included  in  the  predicate  of  this  first 
premise,  and  in  the  conclusion  the  subject  of  the  first  is  denied 


200  LOGIC. 

of  the  subject  of  the  last  premise.  For  example  :  No  A  is  in 
B  ;  all  C  is  in  B,  and  all  D  is  in  C  ;  therefore,  no  A  is  in  D. 

4.  When  some  intermediate  premise  is  given  as  negative, 
and  in  all  the  subsequent  ones  each  successive  conception  is 
given,  as  included  in  or  agreeing  with  the  predicate  of. the 
negative  one,  and  in  the  conclusion  the  subject  of  the  first  is 
denied  of  the  subject  of  the  last  premise.    Example : 

All  A  is  B 
All  B  is  C 
No  C  is  D 
All  E  is  D 
All  F  is  E 
All  G  is  F 
.-.  No  A  is  G. 

Here  all  G  is  given  as  included  in  F,  wliich,  by  the  previous 
conditions,  is  excluded  from  A.  For  the  same  reason,  there- 
fore, that  we  argue  that  no  A  is  in  D,"we  conclude  that  no  A 
is  G.  The  two  last  classes  have  been  entirely  overlooked  by 
logicians  generally.  They  are  as  valid,  however,  as  any  others, 
and  perhaps  as  frequently  employed  in  argument*  In  all  cases 
of  the  negative  sorites,  it  should  be  borne  in  mind,  that  when 
the  first  premise  is  particular  the  conclusion  will  be  particular 
also. 

The  sorites  has  commonly  been  treated  as  a  compound  syllo- 
gism, which  may  be  drawn  out  into  as  many  separate  ones  as 
there  are  intermediate  propositions  between  the  first  and  the 
last.  This  is  true.  The  manner  in  which  we  have  treated  the 
subject,  however,  will  be  seen,  we  judge,  to  be  much  more  sim- 
ple than  this,  and  quite  as  accordant  with  the  principles  of 
science.  If  the  pupil  should  choose  to  reduce  the  sorites  in  the 
manner  indicated,  he  will  bear  in  mind  that  his  first  syllogism, 
in  the  language  of  Dr.  Whately,  "  will  have  for  its  major  the 
second,  and  for  its  minor  the  first,  proposition  of  the  sorites." 


ANALYTIC     OP     SYLLOGISMS.  201 

Section  XI. — Syllogism  of  Chance. 

This  Syllogism  defined. 

The  term  chance  refers  to  the  probability  that  one  of  two  or 
more  uncertain  events  will  occur.  In  induction  and  analogy 
we  have  positive  evidence,  of  greater  or  less  weight,  in  favor 
of  a  given  proposition,  in  distinction  from  all  others.  The  doc- 
trine of  chance  has  place  where,  of  a  given  number  of  events, 
some  one  must  occur,  and  to  us  there  is  the  absence  of  all  posi- 
tive evidence  that  one,  in  distinction  from  the  others,  will  occur. 
The  object  of  the  syllogism  jDf  chance  is  to  announce  the  degree 
of  probability  that  such  an  event  will  occur. 

Principle  which  governs  such  calculations. 

n"  The  probability  that  a  wholly  uncertain  event  will  happen, 
is,"  as  Mr.  Thomson  states,  "  as  the  number  of  cases  in  which 
it  can,  to  the  number  of  those  in  which  it  cannot,  occur." 

The  simplest  case  that  can  be  given,  is  that  in  which  one, 
and  but  one,  of  two  events  must  occur,  and  there  is  an  equal 
uncertainty  which.  In  that  case  the  probabilities  are  equally 
balanced,  and  the  probability  that  either,  in  distinction  from 
the  other,  will  occur,  is  as  one  to  one.  As  the  number  of  pos- 
sible events  is  increased,  the  probability  that  any  one  will  occur 
is  correspondingly  diminished.  Suppose,  on  the  other  hand, 
that  there  are  three  cases,  in  each  of  which  one  of  two  given 
events  must  occur,  and  in  each  case  each  is  equally  probable. 
The  probability  that  one  of  these  events  will  occur  in  one  of  the 
three  cases,  is  as  seven  to  one ;  and  that  it  will  not  occur  in 
each  case  successively,  as  one  to  seven.  Suppose,  further,  that 
there  are  six  events,  each  of  which  is  equal  to  each  of  the 
others  on  the  score  of  probability,  and  that  one  of  these,  to  the 
exclusion  of  each  of  the  others,  must  occur.  The  probability 
that  in  any  given  case  any  one  will  occur,  is  as  one  to  five. 
The  probability  that  in  six  successive  cases  any  one  will  occur, 
at  least  once,  is  as  one  to  one.     The  probability  that  any  one 


• 


will  occur  in  each  of  the  six  successive  cases,  is  as  one  to  forty- 
four  thousand  six  hundred  and  fifty-six.  The  application  of  the 
above  examples  to  cases  in  which  one  of  two  or  more  events 
must  occur,  and  there  is  a  greater  probability  that  one  will 
occur  than  there  is  that  the  other  will,  is  so  obvious,  that 
nothing  need  be  added  on  the  subject. 

The  syllogism  of  chance  is,  also,  often  applied  in  determining 
the  probable  cause  of  given  events.  Suppose  that  some  event, 
X,  has  occurred,  and  that  it  is  known  that  one  of  two  causes, 
A  or  B,  must  have  produced  the  event  referred  to.  Suppose 
that  the  probabilities  in  favor  of  each,  equal  those  in  favor  of 
the  other  ;  then,  the  probability  that  A  is  such  is  one-half,  or  as 
one  to  one.  Suppose  that  there  are  two,  three,  or  four  proba- 
bilities in  favor  of  A  to  one  in  favor  of  B  ;  the  case  would  then 
stand  two,  three,  four,  &c,  to  one,  in  favor  of  A  as  compared 
with  those  in  favor  of  B. 

In  some  instances  the  syllogism  of  chance  gives  a  conclusion 
amounting  to  almost  absolute  certainty  in  favor  of  the  occur- 
rence of  a  given  event.  Suppose  that  there  are  six  distinct 
causes,  either  of  which,  if  present,  will  produce  a  given  event, 
and  that  in  reference  to  each,  there  is  a  perfect  equality  of 
probabilities  of  its  presence  and  absence ;  then  the  probability 
that  said  event  will  occur  is  as  forty-four  thousand  six  hundred 
and  fifty-one  to  one. 

We  have  stated  the  above  cases  to  indicate  the  manner  of 
applying  the  principle  above  presented.  The  application  of  the 
principle  will  be  as  the  nature  and  degree  of  the  probabilities 
and  improbabilities  to  be  taken  into  the  account. 


Section  XII. — Immediate  and  Mediate  Syllogisms. 

All  syllogisms,  of  course,  are  either  immediate  or  mediate. 
"  An  immediate  syllogism,"  in  the  language  of  Kant,  "  is  the 
deduction  of  one  judgment  from  another  without  any  inter- 
mediate judgment.  A  syllogism,  where,  besides  the  concep- 
tion which  a  judgment  contains,  other  conceptions  are  used, 


ANALYTIC     OF      SYLLOGISMS.  203 

for  the  purpose  of  deriving  a  cognition  from  them,  is  me- 
diate." 

The  principle  on  which  all  immediate  syllogisms  rest,  is  this  : 
Whatever  is  necessarily  implied  in  an  admitted  judgment,  must 
also  be  admitted.  If,  for  example,  we  admit  the  judgment 
A=B,  as  valid,  we  must  admit  that  A  and  B  both  exist; 
that  they  belong  to  the  same  class  of  objects ;  have  the  same 
fundamental  characteristics;  that  all  objects  with  which  one 
agrees  or  disagrees,  the  other  agrees  or  disagrees  with,  in  a 
similar  manner,  &c,  &c. 

Nothing  is  of  greater  importance  in  reasoning,  than  a  cor- 
rect use  of  the  immediate  .syllogism.  Many  individuals,  when 
they  have  established  a  given  conclusion,  do  not  know  what 
use  to  make  of  it,  because  they  do  not  perceive  what  is  implied 
in  it.     The  mediate  syllogism  has  already  been  elucidated. 


Section  XIII. — The  Peosyllogism  and  Episyllogism. 

A  process  of  reasoning  which  consists  of  but  one  syllogism  is 
simple.  When  it  consists  of  several  syllogisms,  as  in  the  sorites 
already  treated  of,  it  is  compound.  A  compound  syllogism,  in 
which  the  various  syllogisms  are  in  subordination,  the  first  to 
its  successors  or  the  reverse,  is  called  a  concatenation  of  syllo- 
gisms. Of  this  class  of  compound  syllogisms  we  need  only 
allude  to  two  kinds,  in  addition  to  those  already  considered : 
the  prosyllogism  and  the  episyllogism. 

When,  in  a  chain  of  reasoning,  one  of  the  premises  of  the 
main  argument  is  the  conclusion  of  another  syllogism,  the  lat- 
ter is  called  the  prosyllogism.  When,  on  the  other  hand,  the 
conclusion  of  the  main  argument  is  made  the  premise  of  a  sup- 
plementary one,  this  last  is  called  the  episyllogism.  The  fol- 
lowing illustration  of  these  two  forms  of  the  syllogism  we  take 
from  "  Thomson's  Laws  of  Thought :" — "  Let  us  take  the  syllo- 
gism which  a  coroner's  jury  might  have  to  go  through.  The 
questioais,  '  Has  A  B  been  poisoned  ?'  and  the  syllogism  is, 
A  man  who  has  taken  a  large  quantity  of  arsenic  has  been 


204  LOGIC. 

poisoned  ;'  and  A  B  is  found  to  have  done  so ;  therefore,  he  is 
poisoned :"  with  the  addition  of  a  prosyllogism  and  episyllo- 
gism  the  reasoning  would  run : — "  A  man  who  has  taken  ar- 
senic has  heen  poisoned ;  and  A  B  has  taken  arsenic,  for  the 
application  of  Marsh's  and  Reinsch's  tests  discover  it  (pro- 
syllogism)  ;  therefore,  A  B  has  been  poisoned,  and,  therefore, 
we  cannot  return  a  verdict  of  death  from  natural  causes  (epi- 
syllogism)." 


Section  XIV. — Syllogism   of   Classification. 

Classification,  to  a  greater  or  less  extent,  enters  into  all  the 
sciences,  and  constitutes  the  exclusive  basis  of  some  of  them ; 
such  as  mineralogy,  zoology,  and  botany.  The  science  of  logic, 
therefore,  would  be  incomplete,  did  it  not  include  a  develop- 
ment of  the  principles  and  laws  of  this  one  department  of  the 
laws  of  thought. 

principles  and  laws  of  this  form  of  the  syllogism. 

Two  questions,  entirely  distinct  the  one  from  the  other,  enter 
into  all  investigations  in  this  department  of  science,  to  wit,  the 
conditions  on  which  any  individuals  may  take  rank  as  members 
of  any  given  class  ;  and  what  may  be  validly  affirmed  and  de- 
nied of  them,  in  consequence  of  the  ascertained  fact,  that  they 
belong  to  said  class.  In  regard  to  the  first  question,  we  would 
remark,  that  each  class  has  its  special  tests  or  marks,  that  is, 
characteristic  conception.  Any  individual  must,  as  a  title  to 
admission  into  the  class,  reveal,  as  possessed  by  himself,  the 
elements  represented  in  this  one  conception.  In  this  depart- 
ment the  syllogism  of  classification  may  be  thus  represented  : 

Every  individual  having  these  characteristics  belongs  to  this  class  ; 

A  has  these  characteristics  ; 

A,  therefore,  belongs  to  this  class. 

Then  every  class  is  represented  by  a  specifical  or  generical  con- 
ception, as  the  case  may  be ;  a  conception  which  includes  all 


ANALYTIC     OP     SYLLOGISMS.  205 

the  elements  embraced  in  the  characteristic  conception,  and  all 
others  strictly  common  to  every  individual  of  the  class  referred 
to.  When  it  has  been  ascertained,  through  the  characteristic 
conception,  that  an  individual  belongs  to  a  certain  class,  then 
we  may  reason  from  this  fact  to  his  general  characteristics  as  a 
member  of  such  class,  and  may  affirm  of  him  any  elements  em- 
braced in  the  specifical  conception  of  that  class,  or  in  any  of  its 
superior  or  generical  conceptions.  In  this  department,  the  syl- 
logism of  classification  runs  thus  : 

All  members  of  this  class  have  these  characteristics  ; 

A  is  a  member  of  this  class  ; 

A,  therefore,  has  these  characteristics. 

Take,  in  illustration,  the  case  of  the  coroner's  inquest  referred 
to  in  another  connection.  An  individual  has  died  in  circum- 
stances which  indicate  the  fact,  that  he  was  poisoned.  On  a 
post-mortem  examination,  a  certain  substance,  which  resembles 
in  external  appearance  arsenic,  is  found  in  his  stomach.  Tests 
are  applied  to  determine  the  nature  of  that  substance.  The  re- 
sult is  the  inference,  that  it  is  arsenic.  The  form  of  the  syllo- 
gism yielding  this  deduction  was  this : 

Every  substance  answering  certain  tests  is  arsenic  ; 
This  substance  answers  these  tests  ; 
It  is,  therefore,  arsenic. 

This  fact  being  thus  ascertained,  the  verdict  is  now  rendered 
in  accordance  with  this  syllogism  : 

Every  individual  with  a  given  amount  of  arsenic  in  his  stomach  is  poisoned  ; 
This  individual  was  in  that  state  ; 
Therefore,  he  was  poisoned. 

The  syllogism  through  which  the  properties  of  this  substance 
is  inferred,  the  fact  that  it  is  arsenic  having  been  ascertained, 
may  be  thus  expressed : 

Arsenic  is  poison  ; 

This  substance  is  arsenic  ; 

Therefore,  it  is  poison. 

Kote. — The  correctness  of  the  above  view  of  the  syllogism 


of  classification  will  not  be  doubted.  Yet  this  view  frees  the 
syllogism,  in  all  its  forms,  from  an  objection  of  pelitio  principii 
and  idle  tautology  already  referred  to,  which  has  been  urged 
against  it,  the  above  being  the  only  form  against  which  the  ob- 
jection even  apparently  holds.  The  objection  is  this,  that  in  the 
conclusion  nothing  is  asserted  but  what  had,  in  form,  been  pre- 
viously asserted  in  the  premises.  The  objection  overlooks  the 
fact,  that  the  minor  premise,  as  in  the  case  last  given  (the  form 
in  which  the  syllogism  is  commonly  stated),  is  the  conclusion  of 
a  prosyllogism  in  which  the  truth  of  this  premise  is  affirmed, 
and  that  as  the  result  of  investigation. 

CONCLUDING  EXPLANATIONS. 

The  following  extract  from  Dr.  Whately  contains  some  im-- 
portant  explanations  demanding  especial  attention,  and  with 
this  extract  we  conclude  our  analytic  of  the  syllogism  : 

"  There  are  various  other  abbreviations  commonly  used, 
which  are  so  obvious  as  hardly  to  call  for  explanation  :  as 
where  one  of  the  premises  of  a  syllogism  is  itself  the  conclusion 
of  an  enthymeme  which  is  expressed  at  the  same  time ;  e.  g. 
'  All  useful  studies  deserve  encouragement ;  logic  is  such  {since 
it  helps  us  to  reason  accurately),  therefore  it  deserves  encour- 
agement ;'  here  the  minor  premise  is  what  is  called  an  enthyme- 
matic  sentence.  The  antecedent  in  that  minor  premise  (i.  e. 
that  which  makes  it  enthymematic)  is  called  by  Aristotle  the 
prosyllogism. 

"  It  is  evident  that  you  may,  for  brevity,  substitute  for  any 
term  an  equivalent ;  as  in  the  last  example,  '  itf  for  '  logic ;' 
'  such,''  for  '  a  useful  study,'  &c.  The  doctrine  of  conversion 
furnishes  many  equivalent  propositions,  since  each  is  equiva- 
lent to  its  illative  converse.  The  division  of  nouns  also  sup- 
plies many  equivalents ;  e.  g.  if  A  is  the  genus  of  B,  B  must 
be  a  species  of  A  ;  if  A  is  the  cause  of  B,  B  must  be  the  effect 
of  A. 

"  And  many  syllogisms,  which  at  first  sight  appear  faulty, 
will  often  be  found,  on  examination,  to  contain  correct  reason- 


ANALYTIC     OF     SYLLOGISMS.  207 

ing,  and,  consequently,  to  be  reducible  to  a  regular  form  ;  e.  g. 
when  you  have,  apparently,  negative  premises,  it  may  happen, 
that  by  considering  one  of  them  as  affirmative,  the  syllogism 
will  be  regular :  e.  g.  '  No  man  is  happy  who  is  not  secure  ; 
no  tyrant  is  secure;  therefore,  no  tyrant  is  happy,'  is  a  syl- 
logism in  Celarent*  Sometimes  there  will  appear  to  be  too 
many  terms ;  and  yet  there  will  be  no  fault  in  the  reason- 
ing, only  an  irregularity  in  the  expression  :  e.  g..  '  No  irra- 
tional agent  could  produce  a  work  which  manifests  design  ; 
the  universe  is  a  work  which  manifests  design  ;  therefore,  no 
irrational  agent  could  have  produced  the  universe.'  Strictly 
speaking,  this  syllogism  has  five  terms  ;  but  if  you  look  to  the 
meaning,  you  will  see,  that  in  the  first  premise  (considering  it 
as  a  part  of  this  argument)  it  is  not,  properly,  '  an  irrational 
agent'  that  you  are  speaking  of,  and  of  which  you  predicate 
that  it  could  not  produce  a  work  manifesting  design  ;  but 
rather  it  is  this  '  work,'  &c.  of  which  you  are  speaking,  and  of 
which  it  is  predicated  that  it  could  not  be  produced  by  an  irra- 
tional agent ;  if,  then,  you  state  the  propositions  in  that  form, 
the  syllogism  will  be  perfectly  regular. 

"  Thus,  such  a  syllogism  as  this,  '  Every  true  patriot  is  disin- 
terested ;  few  men  are  disinterested ;  therefore,  few  men  are 
true  patriots ;'  might  appear  at  first  sight  to  be  in  the  second 
figure,  and  faulty  ;  whereas  it  is  in  Barbara,  with  the  premises 
transposed  /  for  you  do  not  really  predicate  of '  feAV  men,'  that 
they  are  '  disinterested,'  but  of  ' disinterested  persons]  that  they 
are  '  few.'  Again  :  '  None  but  candid  men  are  good  reasoners ; 
few  infidels  are  candid ;  few  infidels  are  good  reasoners.'  In 
this  it  will  be  most  convenient  to  consider  the  major  premise  as 
being,  '  all  good  reasoners  are  candid'  (which,  of  course,  is  pre- 
cisely equipollent  to  its  illative  converse  by  negation) ;  and  the 

*  If  this  experiment  be  tried  on  a  syllogism  which  has  really  negative  premises,  the  only 
effect  will  be  to  change  that  fault  into  another,  viz.,  an  excess  of  terms,  or  (which  is  sub- 
stantially the  same)  an  undistributed  middle;  e.  g.  "an  enslaved  people  is  not  happy;  the 
English  are  not  enslaved ;  therefore,  they  are  happy ;''  if  "  enslaved"  be  regarded  as  one  of 
the  terms,  and  "not  enslaved"  as  another,  there  will  manifestly  be  four.  Hence  you  may 
Bee  how  very  little  difference  there  is  in  reality  between  the  different  faults  which  are  enu- 
merated. 


208  LOGIC. 

minor  premise  and  conclusion  may,  in  like  manner,  be  fairly  ex- 
pressed thus :  '  Most  infidels  are  not  candid ;  therefore,  most 
infidels  are  not  good  reasoners ;'  which  is  a  regular  syllogism 
in  Camestres*  Or,  if  you  would  state  it  in  the  first  figure, 
thus :  '  Those  who  are  not  candid  (or  uncandid)  are  not  good 
reasoners ;  most  infidels  are  not  candid ;  most  infidels  are  not 
good  reasoners.' " 

*  The  reader  is  to  observe  that  the  term  employed  as  the  subject  of  the  minor  premise, 
and  of  the  conclusion,  is  "  most-infidels ;"  he  is  not  to  suppose  that  "  most"  is  a  sign  of  dis- 
tribution ;  it  is  merely  a  compendious  expression  for  "  the  greater  port  of." 


PART  II. 

THE  DIALECTIC,  OR  DOCTRINE  OF  FALLACIES. 


Fallacy  defined. 

A  fallacy,  as  the  term  is  generally  understood,  "  is  any  un- 
sound mode  of  arguing  which  appears  to  demand  conviction, 
and  to  be  decisive  of  the  question  hi  hand,  when  in  fairness  it  is 
not."  In  the  present  treatise  the  term  fallacy  will  be  employed 
to  represent  any  intellectual  process  held  as  valid  for  the  truth 
to  which  it  pertains,  but  which  is,  in  fact,  not  thus  valid.  We 
know  well,  that  what  is  not  true  may  be  defended  by  arguments 
apparently  sound  or  unsound,  and  truth  itself  may  be  defended 
by  invalid  arguments.  In  our  treatment  of  this  subject,  it  will 
be  our  object  to  develop  the  characteristics  of  such  invalid  pro- 
cedures, characteristics  by  which  they  are  distinguished  from 
processes  which  must  be  received  as  valid. 

Fallacies  where  found. 

If  we  take  any  argument  which  is  not  valid,  it  is  self-evident 
that  the  defect  in  it  must  consist  in  the  conceptions  themselves, 
in  the  relations  affirmed  to  exist  between  such  conceptions  in 
the  premises  ;  in  a  want  of  connection  between  such  premises 
and  the  conclusions  deduced  from  them  ;  or,  in  two  or  more  of 
these  defects  combined.  Every  valid  process,  as  we  have  al- 
ready shown,  has  the  following  characteristics,  to  wit :  the  con- 
ceptions are  constituted  exclusively  of  real  intuitions  relating 
to  the  objects  of  such  conceptions  ;  the  premises  present  nothing 


but  real  relations  existing  between  the  conceptions  themselves ; 
and  the  conclusion  is  the  necessary  consequent  of  the  relations 
given  in  the  premises. 

The  question  to  be  determined  is,  How  does  error  enter  into 
one  or  the  other  department  of  such  process,  or  into  two  or 
more  of  them  together  ?  When  this  question  is  resolved,  the 
object  of  the  dialectic  will  be  accomplished. 

The  ultimate  cause  and  source  of  Error. 

Were  man  a  pure  intelligence,  with  no  sensibility  or  Avill, 
error  to  him  would  be  impossible.  Every  intellectual  move- 
ment would  be  determined  by  fixed  and  immutable  laws,  and 
would  always  accord  with  the  facts  presented.  Knowledge 
would  be  limited,  but  free  from  error.  The  real  source  of  error 
is  false  assumption.  This  we  have,  as  we  judge,  fully  estab- 
lished in  the  treatise  on  the  will.  As  pure  intelligents  we  can- 
not affirm,  without  adequate  evidence,  that  things  are  or  are 
not  so  and  so.  In  the  absence  of  such  evidence,  however,  we 
may  assume  that  they  are,  and  act  accordingly.  Similar 
assumptions  may  be  made  in  regard  to  all  the  antecedents 
and  consequents  of  the  one  assumption  referred  to.  Thus  long 
trains  of  error  may  be  introduced  into  all  our  intellectual  pro- 
cedures. Without  further  preliminary  observations,  Ave  will 
now  proceed  in  our  exposition  of  the  doctrine  of  fallacies,  and 
will  begin  with  the  phenomena  of  thought  in  which  error  first 
appears,  to  wit,  conceptions. 


DOCTRINE     OF     FALLACIES.  211 

CHAPTER  I. 

INVALID    CONCEPTIONS. 

A  conception,  as  we  have  seen,  is  valid  when,  and  only 
when,  it  is  constituted  of  elements  really  given  by  intuition 
Relatively  to  its  object,  that  is,  such  conceptions  only  can  be  em- 
ployed as  subjects  and  predicates  of  valid  judgments.  Take,  as 
an  illustration,  the  proposition  or  judgment,  "  Every  A  is  B." 
This  judgment  can  be  valid  but  upon  the  condition,  that  the 
conceptions  represented  by  these  terms  are  constituted  of 
nothing  but  real  intuitions  relative  to  their  respective  objects. 
If  elements  not  thus  given  have  been  introduced  into  these 
conceptions,  that  fact  may  wholly  vitiate  the  judgment  under 
consideration. 

Almost,  if  not  quite,  universally,  permit  us  to  remark  further, 
conceptions  are  constituted  of  some  elements  really  given  by 
intuition.  A  conception,  none  of  whose  elements  were  thus 
given,  can  hardly  be  found.  They  become  vitiated  only  by 
the  introduction  into  them  of  elements  not  thus  given.  At  the 
basis  of  such  conceptions,  also,  whether  they  are  really  valid  or 
not,  there  is  an  assumption  that  they  represent  their  objects  as 
they  are,  or  rather  that  such  conceptions  are  constituted  ex- 
clusively of  elements  given  by  intuition  relatively  to  their 
objects. 

The  question  to  be  determined  is,  How  do  invalid  elements 
come  to  be  intermingled  with  valid  ones,  in  conceptions  as- 
sumed as  valid  throughout,  for  their  objects  ?  We  are  now 
prepared  to  resolve  this  question.  Among  the  most  fruitful 
causes  of  vitiated  conceptions  we  notice  the  following  : 

SOURCES   OF   INVALID   CONCEPTIONS. 

1.  The  action  of  the  Imagination  in  peculiar  circumstances. 
We  meet,  for  example,  a  stranger ;    some  incident  connected 


with  him  makes  a  very  pleasing  impression  upon  our  minds. 
Through  the  action  of  the  associating  principle  every  other  ele- 
ment that  is  pleasing  in  character  is  suggested  to  our  minds, 
and  these  elements,  by  the  action  of  the  imagination,  are  all 
Wended  into  one  conception,  which  we  thus  assume  as  truly 
representing  the  real  character  of  this  individual.  This  con- 
ception now  becomes  the  basis  of  an  endless  diversity  of  judg- 
ments relative  to  the  individual  referred  to.  In  view  of  the 
diverse  elements  of  the  conception,  we  rank  the  individual  with 
the  noble,  the  honorable,  the  truthful,  the  generous,  &c,  of  the 
race,  and  separate  him  from  all  classes  of  an  opposite  character, 
denying  of  him  all  characteristics  incompatible  with  the  ele- 
ments of  the  conception  thus  formed  of  him. 

If  the  incident  referred  to  happens  to  be  a  displeasing  one, 
by  the  action  of  the  principle  named,  an  opposite  conception  is 
formed,  a  characteristic  conception,  which  becomes  the  basis 
of  corresponding  judgments,  affirmative  and  negative. 

Now,  if  we  go  back  and  analyze  this  conception,  we  shall 
find  that  but  one  element  in  it  was  really  given  by  intuition,  to 
wit,  the  single  incident  referred  to.  So  far  only  is  said  con- 
ception, whether  it  happens  to  correspond  with  its  object  or 
not,  valid,  relatively  to  us,  as  the  basis  of  judgments  in  respect 
to  the  individual  referred  to.  On  an  endless  diversity  of  sub- 
jects are  invalid  and  vitiated  conceptions  introduced  into  the 
mind,  through  the  action  of  the  principle  under  consideration. 
Science  itself  is  not  free,  in  many  of  its  departments,  from  such 
conceptions. 

Desire,  also,  fear,  and  other  kindred  affections,  often  operate 
in  connection  with  the  same  principle  to  induce  invalid  concep- 
tions. Such  states  of  mind,  through  the  action  of  the  asso- 
ciating principle,  suggest  all  elements  of  thought  which  accord 
with  the  existing  state  of  consciousness,  and  those  elements, 
through  the  action  of  the  imagination,  are  blended  into  corre- 
sponding conceptions.  These  are  assumed  as  valid,  and  as  such 
become  the  determining  causes  of  corresponding  judgments 
and  deductions.  When  we  come  to  examine  such  processes 
we  find  them  invalid,  because  the  main  elements  of  the  concep- 


DOCTRINE     OP     FALLACIES.  213 

tions  which  lay  at  the  foundation  of  the  whole  procedure  were 
not  intuitions,  as  they  should  have  been. 

2.  False  conceptions  are  often  induced  through  the  action  of 
the  suggestive  and  conceptive  principle,  in  connection  with  our 
own  internal  experience,  or  in  connection  with  the  facts  of  our 
own  consciousness. 

Suppose  that  in  our  experience  certain  acts  or  courses  of 
conduct  have,  in  fact,  been  connected  with  and  induced  by 
certain  mental  states,  motives,  or  intentions.  When  we  per- 
ceive the  same  acts  performed  by  others,  we  naturally  conceive 
of  them  as  acting  from  the  same  motives,  and  as  naturally 
assume  this  to  be  true  in  fact.  Hence  all  our  judgments  and 
deductions  in  regard  to  them  are  determined  by  such  concep- 
tions. A  man  whose  external  acts  are  honorable,  benevolent, 
and  virtuous,  and  who  is  conscious  of  acting  from  correspond- 
ing intentions,  naturally  conceives  of  all  others  whose  acts,  as 
known  to  him,  are  of  a  similar  character,  as  acting  from  similar 
intentions.  The  man  whose  motives,  even  in  acts-  honorable  in 
themselves,  are  corrupt,  naturally  conceives  of  all  others  as  be- 
ing, like  himself,  corrupt  and  hypocritical,  even  in  such  acts, 
and  reveals  his  own  want  of  moral  principle  in  his  inrpeachment 
of  the  motives  of  others.  How  often  do  we  find  ourselves  to- 
tally misled  by  conceptions  thus  formed,  and  assumed  as  valid 
relative  to  their  objects.  The  facts  given  by  intuition  are  in 
no  sense  necessarily  connected  with  those  presented  by  the 
associating  principle,  yet  a  large  portion  of  our  practically  gov- 
erning conceptions  are  thus  formed. 

3.  Similar  conceptions  often  arise  as  the  result  of  external 
experience  and  observation.  Suppose  that  in  our  experience 
certain  antecedents  or  consequents  have  uniformly  happened  to 
attend  certain  occurrences,  though  the  connection  between 
them  is  in  no  form  necessary  in  itself,  or  thus  uniform  in  the 
experience  of  others.  Such  an  experience  often  induces  the 
conception  of  these  events  as  sustaining  the  relations  to  each 
other  of  cause  and  effect,  that  is,  as  necessarily  connected.  It 
is  thus,  consequently,  that  they  are  subsequently  employed  as 
the  basis  of  judgments  and  deductions.     So  when  certain  quali- 


214  LOGIC. 

ties  have,  in  our  observation  and  experience,  been  found  con- 
nected with  certain  others,  they  come  often  to  be  related  in  our 
conceptions  as  parts  of  given  wholes.  Hence  when  any  of  these 
qualities  are  perceived,  the  rest  are  conceived  as  present  also, 
that  is,  the  presence  of  the  wholes  referred  to  is  apprehended 
and  inferred.  Yet,  on  investigation,  these  qualities  are  found 
to  have  no  necessary  connection,  and  their  connection  in  our 
observation  and  experience  to  have  been  merely  accidental. 

4.  Public  rumor  and  opinion  often  become  the  sources  of 
false  conceptions.  We  find  a  certain  conception  religious,  so- 
cial, political,  or  scientific,  taken  for  granted  in  the  circle  in 
which  Ave  are  accustomed  to  move.  How  often,  without  being 
investigated  at  all,  does  it  assume  a  similar  place  in  our  minds, 
and  thus  determine/  our  judgments  and  deductions  in  all  such 
departments  of  thought !  So  when  an  individual  has  attained  to 
a  certain  reputation,  good  or  bad,  with  the  public,  individuals, 
without  a  knowledge  of  the  facts,  receive  that  reputation  as  the 
determining  standard  of  their  judgments  in  regard  to  him. 
Yet  subsequent  facts  may  show  that  the  conception  thus  in- 
duced is  wholly  false.  On  questions  of  importance,  no  person  is 
safe  in  relying  upon  conceptions  thus  derived  as  the  basis  of 
judgments  and  deductions. 

5.  The  results  of  false  information  or  scientific  deductions 
often  are  embodied  subsequently  as  elements  of  conceptions, 
and  thus  lay  the  foundation  of  false  judgments  and  deductions 
on  the  most  important  subjects.  At  one  time  it  was  a  received 
deduction  of  science,  for  example,  that  the  earth  is  the  centre 
of  the  solar  system — the  centre  around  which  the  sun,  and  stars, 
and  planets,  all  revolve.  The  conception  of  the  universe  thus 
deduced  determined,  while  thus  received,  all  subsequent  judg- 
ments and  deductions  in  the  science  of  astronomy.  How  long 
did  the  sensational  theory,  the  theory  of  Locke,  given  as  the  re- 
sult of  scientific  deduction,  determine  the  judgments  and  de- 
ductions of  philosophers  and  theologians  too ;  and  that  in  refer- 
ence to  the  universe,  God,  duty,  and  immortality.  Of  two  dis- 
tinct and  opposite  conceptions  pertaining  to  the  human  will,  the 
one  or  the  other  of  which,  that  of  liberty  or  necessity,  must  be 


DOCTEINE     OF     FALLACIES.  215 

true,  the  one  which  we  do  receive  will  and  must  determine  the 
character  of  all  our  subsequent  judgments  and  deductions,  in  the 
whole  field  of  mental  and  theological  science.  Suppose  that  our 
conceptions  on  this  subject  are  the  result  of  false  deductions, 
while  this  result  remains  it  will  be  impossible  for  us  to  reason 
correctly  on  the  most  important  questions  in  the  most  impor- 
tant of  all  sciences,  that  of  God,  duty,  and  immortality.  We 
refer  to  such  examples  simply  in  illustration  of  the  principle  un- 
der consideration,  the  influence  of  false  deductions  in  science  in 
determining  the  character  of  conceptions  which  lie  at  the  foun- 
dation of  subsequent  judgments  and  reasoning. 

6.  We  mention  but  one  other  cause  of  false  conceptions, 
wrong  interpretations  of  authoritative  documents,  such  as  the 
sacred  Scriptures,  the  constitution  and  laws  of  our  government, 
&g.  A  certain  exposition,  false  in  itself,  we  will  suppose  has 
been  given,  and  subsequently  comes  to  be  received  as  the  valid 
conception  of  the  real  meaning' of  the  document.  Whenever 
thought  is  subsequently  turned  to  said  document,  the  concep- 
tion under  consideration  will  stand  between  the  mind  and  the 
document,  and  the  mind  will  see  nothing  in  the  latter  but  what 
previously  existed  in  the  former.  All  subsequent  applications 
of  the  principles  of  the  document  will  also  be  determined  by 
this  conception.  Thus  it  often  happens,  that  truth  as  it  is  in 
itself,  is,  for  ages,  veiled  from  the  human  mind  by  false  concep- 
tions induced  as  above  stated.  In  the  above  classification  we 
have  simply  indicated  the  sources  and  influence  of  false  concep- 
tions, and  will  leave  the  reader  to  complete  what  has  here  been 
commenced. 


216 


CHAPTER  I. 

THE    DIALECTIC  — INVALID    JUDGMENTS. 

We  now  advance  to  a  consideration  of  invalid  judgments  or 
propositions.  "We  have  already  given  the  criteria  of  valid  judg- 
ments. Invalid  judgments  are  exclusively  assumptive,  and  con- 
sist of  problematical  judgments  assumed  as  already  established 
as  true,  or,  of  judgments  false  in  themselves,  and  assumed  as 
true.  We  shall  endeavor  to  indicate  the  sources  of  such  judg- 
ments. Among  these  we  adduce  the  following  as  deserving 
especial  notice : 

Section  I. — Problematical   Judgments  assumed  as   First 
Truths. 

The  first  that  we  notice  is  a  certain  class  of  assumptions  in 
which  mere  problematical  judgments,  those  which  are  neither 
self-evident  nor  yet  established  as  true  by  valid  evidence,  are 
ranked  among  primary  and  necessary  intuitions.  Hitherto  we 
have  had  no  very  definite  and  decisive  criteria  of  first  truths, 
those  commonly  given  being  rather  accidents  than  fundamental 
characteristics  of  such  truths.  The  criteria  given  in  the  Ana- 
lytic of  Judgments  will  enable  the  student,  we  judge,  readily  to 
distinguish  such  truths  from  assumptions  which  have  no  claims 
to  be  ranked  among  primary  intuitions.  The  criteria  to  which 
we  refer,  it  will  be  recollected,  is  this,  "  All  valid  primary  intui- 
tions or  first  truths  are,  exclusively,  analytical  judgments]'' 
judgments  in  which  the  conception  represented  by  the  predi- 
cate is  an  essential  element  of  that  represented  by  the  subject ; 
as  in  the  proposition;  "  All  bodies  are  extended  ;"  or  in  which 
the  conception  represented  by  the  former  term  is  the  logical 
antecedent  of  that  represented  by  the  latter,  as  in  the  principle, 
" Body  supposes  space,  succession,  time,"  &c.  Now  nothing  is 
more  common  than  for  mere  problematical  judgments  which 


DOCTRINE     OF     FALLACIES.  21V 

have  no  such  characteristics,  and  which  are  even  false,  in  fact, 
to  be  assumed  as  first  truths  of  science,  and  to  be  used  as  such 
in  the  formation  of  systems  and  the  explanation  of  facts.  We 
will  give  a  few  examples  in  illustration. 

Assumption  that  a  thing  cannot  act  where  it  is  not. 

Let  us  first  notice  the  following  assumption  of  Sir  Isaac  New- 
ton, and  presented  by  this  great  philosopher  as  a  primary  intui- 
tion :  "  It  is  inconceivable  that  inanimate  brute  matter  should, 
without  the  mediation  of  something  else  which  is  not  material, 
operate  upon  and  affect  ottter  matter  Avithout  mutual  contact." 
The  opposite  supposition  he  affirms  to  be  "  too  great  an  absur- 
dity" to  be  believed  by  any  one  "  who,  in  philosophical  matters, 
has  a  competent  faculty  of  thinking."  Whence  this  assump- 
tion ?  Is  it,  like  extension,  an  essential  element  of  our  concep- 
tion of  this  substance  ?  Or,  is  it  the  logical  antecedent  of  our 
conception  of  that  substance,  or  of  any  element  of  that  concep- 
tion ?  By  no  means.  It  has  not  a  shadow  of  a  right  to  a  place 
among  the  first  truths  of  science.  Nor  is  its  truth  even  remote- 
ly indicated  by  any  of  the  known  phenomena  of  this  substance. 
It  is  nothing  but  a  mere  assumption,  unauthorized  by  any  form 
of  evidence,  mediate  or  immediate. 


The  assumption  that  our  knowledge  of  matter  is 
mediate. 

Let  us  next  contemplate  the  assumption,  that  all  our  know- 
ledge of  matter  is  exclusively  mediate  or  representative,  being 
derived  through  the  consciousness  of  sensation,  and  not  in  any 
form  or  respect  immediate  or  presentative.  How  did  this  as- 
sumption ever  obtain  a  place  in  science  ?  Not  as  the  result  of 
logical  deduction  from  the  facts  of  consciousness.  This  none 
will  affirm.  ,  We  know  of  no  professed  logical  demonstration  of 
its  truth.  It  has  always,  when  received,  been  assumed  as  a 
first  truth,  and  has,  as  such  an  assumption,  taken  its  place  as  a 
principle  in  science.  What  claim  has  this  assumption  to  this 
10 


high  position  ?  We  certainly  cannot  find  it  by  any  analysis  of 
our  fundamental  conceptions  of  matter,  on  the  one  hand,  or  of 
mind,  on  the  other.  ~No  man  can  affirm,  a  priori,  from  what  he 
knows  of  this  substance,  that  the  former  cannot  be  to  the  latter 
the  object  of  immediate  or  presentative  knowledge.  Nor  can 
we  affirm  it,  in  a  similar  manner,  from  the  fact  of  the  mind's 
present  connection  with  the  body.  Nor  is  its  truth  the  logical 
antecedent  of  any  elements  of  our  conceptions  of  mind  and  mat- 
ter, or  of  any  of  the  facts  of  consciousness.  On  the  other  hand, 
if  we  are  conscious  of  any  thing,  we  are  conscious  of  a  direct  and 
immediate  or  presentative  knowledge  of  this  substance.  The 
most  that  can  be  said  of  this  judgment  is,  that  it  is  a  mere  pro- 
blematical judgment,  wholly  incapable,  from  the  nature  of  the 
case,  of  proof.  Yet,  as  a  first  truth,  whole  systems  of  physical, 
mental,  and  theological  science  have  been  founded  upon  and 
determined,  in  all  their  fundamental  characteristics,  by  it.  All 
that  we  now  are  called  upon  to  do  is,  in  the  name  of  science,  to 
challenge  the  right  of  this  assumption  to  the  place  which  it  has 
so  long  occupied,  to  wit,  that  of  a  first  truth  or  principle  in 
science.  To  such  a  position  it  has  no  claims.  When,  as  a  theo- 
rem, its  truth  has  been  demonstrated,  then,  and  not  before,  can 
it  have  any  legitimate  place  in  science. 

Fundamental  and  opposite  Assumptions  of  Materialism  and 
Idealism. 

We  now  refer  to  two  distinct  and  opposite  assumptions,  the 
first  of  which  lies  at  the  basis  of  Materialism,  and  the  second  at 
that  of  Idealism.  Materialism  rests  exclusively  upon  the  as- 
sumption, that  all  our  knowledge  is  derived  exclusively  through 
sensation  or  external  perception,  and  that,  consequently,  nothing 
but  the  external  universe,  with  its  laws,  can  be  to  us  an  object 
of  knowledge,  and  this  whole  system  must  be  false,  unless  the 
validity  of  this  assumption  be  granted.  Idealism,  in  all  its 
forms,  on  the  other  hand,  rests  upon  the  exclusive  assumption, 
that  nothing  can,  by  any  possibility,  be  to  the  mind  an  object  of 
real  knowledge,  but  its  own  operations,  and  this  system,  in  all 


DOCTRINE     OF     FALLACIES.  219 

its  forms,  must  stand  or  fall  with  that  assumption.  Now 
neither  of  these  assumptions  finds  a  place  among  the  principles 
of  science  from  any  a  posteriori  evidence  or  demonstration  of 
its  validity.  In  opposition  to  the  first  assumption,  that  of  mate- 
rialism, we  find  ourselves  in  consciousness  just  as  able  to  distin- 
guish one  mental  state  from  another,  thoughts  from  feelings  and 
acts  of  will,  for  example,  or  one  strong  feeling  or  act  of  will  from 
■bother,  as  we  are  to  distinguish  one  external  object  from 
another.  We  can  as  readily  distinguish  a  thought  from  a  sen- 
sation, emotion,  or  act  of  will,  as  Ave  can  an  elephant  from  a  man, 
or  a  mountain  from  a  molehill.  We  are  just  as  conscious  of  the 
fact  of  perceiving  our  own*  mental  states,  as  we  are  of  having 
similar  perceptions  of  external  objects.  In  opposition  to  the 
assumption  of  idealism,  it  cannot  be  denied  that  we  are  just  as 
conscious  of  the  fact  of  perceiving  external  material  objects,  as 
we  are  of  a  knowledge  of  our  own  mental  states.  In  opposition 
to  both  assumptions,  we  have  precisely  the  same  evidence  of  the 
power  in  ourselves  to  know  one  class  of  phenomena  as  the 
other.  There  can  be,  we  repeat,  no  possible  a  posteriori  proof 
of  the  truth  or  validity  of  either  of  these  assumptions.  Nor  is 
the  validity  of  either  of  them  self  evident ;  nor  can  either  of 
them  be  shown  to  sustain  the  relations  of  logical  antecedents 
to  any  facts  of  consciousness,  nor  to  any  elements  of  our  valid 
conceptions  of  matter,  on  the  one  hand,  or  of  mind  on  the 
other.  To  the  high  position  of  first  truths  or' principles  in 
science,  they  have  not  a  shadow  of  a  claim  in  any  form  what- 
ever. How  can  we  decide  a  priori  that  the  human  intelligence 
may  not,  and  does  not,  possess  the  power  of  real  external  and 
internal  perception  both,  and  that  one  class  of  these  perceptions 
may  not  be,  and  is  not,  just  as  valid  for  the  real  character  of  its 
objects  as  the  other  ?  Not  a  solitary  valid  characteristic  of 
a  first  truth  or  principle  of  science,  can  be  shown  to  attach  to 
either  of  these  assumptions ;  yet,  as  first  truths,  they  have  for 
ages  lain  at  the  basis  of  systems  of  universal  ontology,  meta- 
physics, and  theology.  Now,  in  the  name  of  science,  we  chal- 
lenge the  right  of  each  of  these  assumptions  to  the  place  in 
science  which  has,  for  ages,  been  claimed  for  them.     We  affirm 


that  they  are  mere  assumptions  pushed  forward,  as  self-evident 
primary  intuitions,  into  the  sphere  of  science.  Till  their  validi- 
ty has  been  clearly  demonstrated,  we  deny  the  validity  of  any 
deductions  which  may  have  been  drawn  from  them,  as  princi- 
ples in  science. 


ASSUMPTION     PERTAINING    TO    THE     ORIGIN    OP    OUR    IDEA    OP 
CAUSE    AND    EFPECT. 

There  is  an  assumption  pertaining  to  the  origin  of  our  idea 
of  causation,  an  assumption  originally  set  forth  by  M.  de  Biron, 
of  France,  which  has  since  been  pushed  forward  with  great 
zeal  and  ability  into  the  sphere  of  science,  by  his  successor  in 
the  chair  of  philosophy,  Victor  Cousin,  and  which  is  now  exert- 
ing not  a  little  influence  in  philosophy — an  assumption,  conse- 
quently, which  claims  some  special  notice  in  this  connection. 
We  refer  to  the  assumption,  that  we  originally  derived  the  idea 
of  cause  from  the  consciousness  of  our  own  acts  of  will  as  causes. 
We  give  the  theory  in  the  language  of  Prof.  Tulloch  in  his 
"  Theism  :"  "  This  statement  is  that  of  a  distinguished  French 
philosopher,  M.  de  Biron,  who  has  certainly  the  eminent  merit 
of  having,  in  the  most  elaborate  manner,  fixed  attention  on  the 
theory  of  causation  under  discussion.  It  is  to  this  effect :  '  I 
will  to  move  my  arm,  and  I  move  it.'  This  complex  fact  gives 
us  on  analysis  :  1.  The  consciousness  of  an  act  of  will.  2.  The 
consciousness  of  motion  produced.  3.  The  consciousness  of  the 
relation  of  the  motion  to  the  volition.  This  relation  is  in  no 
respect  a  simple  relation  of  succession.  The  motion  not  merely 
follows  our  will,  or  appears  in  conjunction  with  it,  but  is  con- 
sciously produced  by  it.  The  idea  of  power  or  cause  is  thus 
evolved." 

There  are  two  facts  here  asserted  :  1st.  That  we  have  a  direct 
and  intuitive  consciousness  of  the  fact,  that  the  motion  referred 
to  is  caused  by  the  act  of  will.  2d.  That  it  is  intuitively  im- 
plied in  this  fact,  that  in  and  through  the  consciousness  of  our 
acts  of  will  as  causes,  Ave  originally  obtained  the  idea  of  cause 
itself.     Hence  this  theory  of  causation  is  being  pushed  forward 


DOCTEINE     OF     FALLACIES.  221 

into  the  sphere  of  science  as  a  first  truth,  an  intuitive  princi- 
ple.    In  reply,  we  remark  : 

1.  That  we  have  here,  in  the  first  place,  an  undeniable  psy- 
chological error.  We  are  not  conscious,  as  a  matter  of  fact,  of 
any  relation  of  cause  and  effect  between  the  act  of  the  will  and 
the  successive  physical  motions  of  our  bodies.  We  are  simply 
and  exclusively  conscious  of  the  act  of  will  itself,  and  of  nothing 
else.  The  motion  of  the  physical  organization  which  follows 
the  act,  is  as  exclusively  an  object  of  external  perception. 
"  Between  the  overt  fact  of  corporeal  movement  which  we  per- 
ceive," says  Sir  William  Hamilton,  "  and  the  internal  act  of  will 
to  move,  of  which  we  are  self-conscious,  there  intervenes  a  series 
of  intermediate  agencies,  of  which  we  are  wholly  unaware  ;  con- 
sequently, we  can  have  no  consciousness,  as  this  hypothesis  men- 
tions, of  any  causal  connection  between  the  external  links  of  this 
chain,  that  is,  between  the  volition  to  move  and  the  arm  mov- 
ing." There  cannot  be  a  more  manifest  psychological  error 
named,  than  this  dogma  presents. 

2.  We  have  precisely  the  same  evidence,  that  other  mental 
states  are  causes  proper  of  .certain  physical  effects,  that  we  have, 
or  can  have,  that  our  acts  of  will  are  such  causes.  Suppose  that 
through  some  thought  or  apprehension,  a  state  of  intense  men- 
tal excitement  is  induced,  a  state  which  is  immediately  followed 
by  a  corresponding  agitation  of  the  physical  system,  and  that 
not  only  independent  of,  but  in  opposition  to,  our  acts  of  will. 
Now  we  have  just  as  much  evidence  that  this  agitation  of  the 
physical  system,  the  flush  or  paleness  upon  the  cheek,  the  trem- 
bling of  limbs,  and  the  quickening  of  the  pulsation,  is  caused  by 
the  state  of  the  sensibility  referred  to,  as  we  have,  or  can  have, 
that  any  movement  of  the  muscular  system  is  caused  by  voli- 
tion ;  and  we  might,  with  the  same  propriety,  affirm,  that  our 
idea  of  causation  was  originally  derived  through  one  of  these 
sources,  as  through  the  other.  For  ourselves,  if  compelled  to 
select  between  these  two  hypotheses,  wre  should  take  the  first ; 
for  we  believe  that,  as  a  matter  of  fact,  the  infant  has  percep- 
tions of  physical  effects  as  connected  with  states  of  the  sensibili- 


222  logic. 

ty  long  before  it  has  any  knowledge  of  them,  as  connected  with 
acts  of  will. 

3.  Not  the  least  indication  of  such  an  origin  can  be  found  in 
the  principle  of  causality  itself,  as  that  principle  exists  in  the 
universal  intelligence,  the  principle,  that  "  Every  event  must 
have  a  cause."  Let  any  one  most  carefully  analyze  this  principle, 
and  he  will  find  in  it  no  indication  whatever  of  any  such  origin. 
What  connection  can  there  be  found  between  the  primary  prin- 
ciple, that  "  Every  event  must  have  a  cause,"  and  the  conscious- 
ness of  an  act  of  will,  and  the  perception  of  a  successive  muscu- 
lar movement,  to  indicate,  that  the  conception  of  the  principle 
originated  in  the  intelligence,  from  the  act  of  consciousness  and 
perception  before  us  ? 

4.  We  remark,  finally,  that  we  need  nothing  but  the  percep- 
tion of  an  event  by  the  mind,  without  any  perception  or  appre- 
hension of  its  particular  or  specific  cause,  to  account  for  the  ori- 
gin of  this  principle  just  as  it  now  exists  in  the  human  intelli- 
gence. The  idea  of  Cause  exists  in  the  intelligence  as  the  logi- 
cal antecedent  of  that  of  an  event,  and  we  find  in  the  intelli- 
gence this  general  power  to  conceive,  when  any  fact  is  given,  of 
the  logical  antecedent  of  that  fact.  The  same  function  of  the 
intelligence  which,  on  the  perception  of  body,  succession,  and 
phenomena,  gives  us  the  logical  antecedents  of  such  perceptions, 
the  idea  of  space,  time,  and  substance,  may,  and  from  its  nature, 
must,  on  the  perception  of  any  event  whatever,  give  us  its  logi- 
cal antecedent,  the  idea  of  cause. 

It  is  just  as  absurd  to  refer  the  origin  of  this  idea  to  the  per- 
ception of  some  one  specific  event,  as  it  would  be  to  refer  the 
origin  of  the  idea  of  space  to  the  perception,  not  of  any  exter- 
nal substance,  whatever  it  may  be,  but  of  some  specific  body,  a 
mountain,  for  example.  Given  in  the  intelligence  any  event 
whatever,  and  the  idea  of  a  cause  must,  from  the  nature  of  the 
reason,  be  originated.  The  inference  deduced  from  this  idea  of 
the  origin  of  the  principle  of  causality  in  the  mind,  will  be  con- 
sidered in  another  connection.  All  that  we  wish  now  to  estab- 
lish is  the  fact,  that  while  the  assumption  under  consideration 
relative  to  the  origin  of  the  idea  of  causation,  has  no  claim  to 


DOCTRINE     OF     FALLACIES.  223 

the  place  of  a  first  truth  or  principle  in  science,  its  validity  has 
not  yet  been  established  by  any  process  of  demonstration  or 
proof,  and  consequently,  that  any  deductions  based  upon  it  are 
without  any  claims  to  our  regard  as  truths  of  science. 

"the  eternal  now"  of  theology. 

We  will  now  consider  an  assumption  which  has  long  held  a 
place  as  an  intuitive  truth  in  the  science  of  theology,  and  which 
has  had  not  a  little  influence  in  the  construction  of  theological 
systems.  We  refer  to  the  assumption,  that  it  is  only  to  finite 
beings  that  events  are,  or»  appear  to  be,  successive ;  that  with 
God,  the  Infinite  and  Perfect,  there  is  no  past,  present,  or  fu- 
ture, but  all  is  alike  present,  "  one  eternal  now."  If  this  is  true 
of  God,  it  must  be  so,  because  events  are  not  really  or  truly  suc- 
cessive, or  because  he  wants  the  power  to  know  them  as  they 
are.  Shall  we  conclude  that  there  is  no  such  thing  as  real  suc- 
cession ?  and  if  so,  by  what  evidence  is  the  truth  of  the  fact 
to  be  established  ?  We  cannot  know  such  a  fact  by  intuition. 
By  what  process  of  argument,  then,  can  its  truth  be  established  ? 
No  one,  we  are  quite  sure,  will  attempt  to  prove  such  a  dogma. 
Shall  we  admit  that  events  are  really  and  truly  successive,  and 
then  limit  and  debase  our  conception  of  the  Most  High  by 
the  assumption,  that  he  wants  the  power  to  know  events  as 
they  are  ? 

Further,  if  events  are  not  really  and  truly  successive,  then  the 
universal  finite  intelligence  is  a  lie,  and  God  stands  convicted  of 
deception  in  thus  constructing  it ;  for  it  affirms  absolutely  the 
reality  of  succession.  If  succession  is  real,  and  our  intelligence 
is  not  a  lie,  and  God  cannot,  as  this  theory  affirms,  distinguish 
the  real  past  from  the  real  present,  or  either  from  the  real  fu- 
ture, then  his  intelligence  is  so  far  less  perfect  than  ours.  One 
question  more  here.  By  what  process  of  intuition  or  deduc- 
tion have  the  advocates  of  this  dogma  attained,  first,  to  the 
stand-point  from  which  the  finite  intelligence  views  events,  and 
then  to  that  from  which  the  Infinite  and  Perfect  views  the 
same,  so  that  they  can  inform  us  how  the  same  things  appear  to 


»       vw  J.HJS        -<-^ 

fUJflVSRSITy 


m^ 


each ;  and  especially  be  able  to  affirm,  that  while  to  the  former 
there  is  real  and  absolute  succession  of  events,  to  the  latter, 
"all  is  one  eternal  now?"  Among  first  truths  or  valid  intui- 
tions, this  dogma  surely  has  no  place.  It  enters  not  as  an  essen- 
tial element  into  our  idea  of  the  Infinite  and  Perfect,  nor  can  it 
be  shown  to  sustain  the  relation  of  logical  antecedent  to  that 
idea,  or  to  any  element  of  it.  It  certainly  exists  not  as  a  truth 
of  inspiration.  This  no  one  will  pretend.  Nor  can  it  be  logi- 
cally deduced  from  any  fact  yet  known  relatively  to  matter  or 
spirit,  to  the  finite  or  the  infinite/  As  a  principle  in  the  science 
of  theology,  it  has  no  place  by  virtue  of  its  claims  as  an  intuitive 
truth,  or  a  valid  deduction  of  science.  This  is  all  that  we  wish 
to  now  say  of  it.  So  far  as  it  has  had  influence  in  theology, 
that  science  has  rested  upon  no  valid  basis.  The  question  for 
its  advocates  to  answer  is  this :  By  what  authority  do  they 
claim  for  this  dogma  a  place  among  the  valid  deductions  of 
science  ?  It  is  especially  as  an  assumed  truth  of  intuition,  how- 
ever, that  we  would  now  challenge  its  validity. 

Assumption  pertaining  to  the  Divine  Personality,  <&c. 

We  now  notice  another  assumption  which  is  being  pushed 
forward  into  the  field  of  science,  as  a  first  truth  or  principle.  It 
is  affirmed  that  personality  and  self-consciousness  cannot  either 
of  them  be  affirmed  of  God,  and  that  for  this  reason  :  they  both 
alike  imply  limitation  in  their  subject,  and  consequently  can 
be  affirmed  only  of  the  finite.  God  is  infinite  and  perfect,  and 
therefore  these  attributes  which  imply  limitation  must  be  de- 
nied of  him.  On  what  ground  can  such  a  dogma  as  this  be  ad- 
mitted ?  Not  surely  as  a  self-evident  truth,  that  is,  as  a  first 
truth  or  principle  in  science.  We  certainly  cannot  intelligently 
affirm  a  priori  that  there  may  not  be,  and  is  not,  a  personality 
really  and  truly  infinite  and  perfect  in  all  his  attributes,  who  is 
distinctly  conscious  of  his  own  perfections  and  relations  as  in- 
finite and  perfect,  and  who  does  possess  a  knowledge  similarly 
perfect  of  all  other  beings  and  objects.  It  is  certainly,  and  that 
in  the  most  emphatic  sense,  limiting  the  Most  High  to  affirm 


DOCTRINE     OF     FALLACII 


the  opposite  of  him.  To  affirm  that  he  is  not,  and  cannot  be, 
absolutely  conscious  of  his  own  perfections,  is  to  limit  his  know- 
ledge to  the  circle  of  the  finite.  Indeed,  it  is  to  exclude  the 
Infinite  and  Perfect  from  the  realm  of  intelligents,  and  to  con- 
fine, that  is,  limit  him  within  the  circle  of  non-intelligents  ;  and 
this  is  the  exclusive  object  of  those  who  are  pushing  this  assump- 
tion into  the  sphere  of  science.  Under  a  professed  veneration 
and  zeal  for  the  honor  of  God,  that  is  affirmed  of  him  which 
utterly  disrobes  him  of  every  attribute  on  account  of  which  he 
can  bo  to  us  an  object  of  real  esteem  or  veneration.  The  Infi- 
nite and  Perfect  is  held  up  before  us  as  characterized  by  in- 
finite ignorance,  instead  of 'absolute  knowledge.  When  the 
advocates  of  this  assumption  have  demonstrated  its  truth  and 
validity,  however,  we  will  admit  it.  To  a  place  among  first 
truths  or  principles  of  science,  the  place  which  its  advocates 
claim  for  it,  it  has  no  claims  whatever.  It  cannot  be  shown  to 
possess  a  solitary  accidental  or  scientific  characteristic  of  any 
such  truth  or  principle. 

We  have  presented  the  above  assumptions  as  examples  in 
illustration  of  the  principle  under  consideration,  to  wit :  the 
error  of  assuming  mere  problematical  judgments,  as  first  truths 
or  intuitive  principles  of  science,  and  then  constructing  systems 
of  knowledge  upon  the  basis  of  such  assumptions.  Others  of  a 
similar  character  might  be  adduced.  Not  one  of  those  which 
we  have  adduced  bears  a  single  characteristic  of  the  class  of 
truths  among  which  they  have  all  been  ranked  by  those  who 
have  constructed  theories  upon  them.  The  reader  should  con- 
tinuously bear  in  mind  the  fact,  that  no  proposition  can  have 
any  claims  to  be  regarded  as  a  first  truth  or  valid  principle  in 
science  which  is  not  strictly  according  to  the  definition  given — 
an  analytical  proposition,  a  proposition  in  which  the  predicate 
represents  an  essential  element  of  the  subject,  as  in  the  proposi- 
tion, "  All  bodies  are  extended  ;"  or  in  which  the  predicate  rep- 
resents the  logical  antecedent  of  the  conception  represented  by 
the  subject,  as  in  the  proposition,  "  Body  sivpposes  space."  It 
is  only  by  usurpation  or  invalid  assumption,  that  any  other  prin- 
ciple or  class  of  principles  can  be  pushed  forward  into  the  sphere 
10* 


226  logic 

of  science  as  a  first  truth.  We  are  -also  to  reject  as  utterly  in- 
valid, all  deductions  resting  upon  any  principles  not  undeniably 
possessed  of  one  or  the  other  of  the  characteristics  above  named. 
One  of  the  highest  demands  of  science  at  the  present  time,  is  a 
fundamental  examination  of  principles  used  as  first  truths  in  the 
construction  of  systems  of  knowledge,  an  examination  in  which 
there  shall  be  a  most  rigid  application  of  the  characteristics 
which  distinguish  all  real  and  valid  intuitions  from  unauthorized 
assumptions,  and  in  which  all  principles  not  having  these  char- 
acteristics shall  be  rejected  as  utterly  invalid.  Till  this  is  done 
the  most  visionary  and  pernicious  theories  will  continue  to  be 
palmed  upon  the  world,  and  held,  by  even  scientific  minds,  as 
embodying  the  highest  forms  and  developments  of  wisdom  and 
knowledge. 


Section  II. — Invalid  Assumptions  pertaining  to  Matters 
of  Fact.* 

Invalid  assumptions  pertaining  to  matters  of  fact  next  claim 
our  attention.     Among  these  we  notice  the  following  : 

1.  False  assumptions  relatively  to  the  authorized  quantity  or 
quality  of  propositions.  Suppose  that  it  has  been  ascertained 
that  a  certain  characteristic  does,  or  does  not,  belong  to  certain 
individuals  of  a  given  class,  and  that  this  is  the  extent  of  our  in- 
duction. The  truth  of  the  subaltern  proposition  I  or  O,  and 
that  only,  has  been  established,  that  is,  we  have  obtained  au- 
thority for  the  judgment,  "  Some  Z  is  X,  or  some  Z  is  not  X," 
and  nothing  more.  Under  such  circumstances,  however,  it  is 
perfectly  common  to  assume  the  truth  of  the  universal  judg- 
ment A  or  E,  as  the  case  may  be ;  that  is,  the  truth  of  the  judg- 
ment, "  All  Z  is  X,  or  no  Z  is  X,"  and  to  use  such  judgments 
as  premises  in  reasoning.     So  when  the  universal  A  or  E  has 

*  The  special  object  of  this  and  the  preceding  section  and  chapter,  is  to  furnish  criteria  by 
which  we  may  judge  correctly,  first,  of  conceptions  employed  in  processes  of  reasoning,  and 
then  of  the  judgments  presented  as  premises.  Upon  all  these  attention  must  be  definitely 
fixed,  and  that  in  the  light  of  valid  criteria,  if  we  would  judge  correctly  of  the  validity  of 
different  processes  of  reasoning. 


DOCTRINE     OF     FALLACIES.  227 

been  ascertained  to  be  untrue,  it  is  perfectly  common  to  assume 
the  truth  of  the  contrary  judgment.  We  have,  for  example, 
examined  some  individuals  of  a  given  class,  and  have  ascertained 
that  they  do,  or  do  not,  possess  certain  characteristics.  All 
that  such  induction  really  authorizes,  is  the  assumption  of  the 
truth  of  the  contradictory  propositions  I  or  O.  It  does  not  au- 
thorize a  denial  of  the  subaltern  judgment,  and  a  consequent 
assumption  of  the  truth  of  the  contrary.  From  the  mere  fact, 
that  A  (All  Z  is  X)  is  false,  Ave  are  not  authorized  to  judge 
that  I  (Some  Z  is  X)  is  also  false,  and  that,  consequently,  E  (No 
Z  is  X)  is  true.  Yet  just  such  judgments  are  perfectly  com- 
mon. The  common  assumption,  that  in  the  process  of  indue* 
tion  we  reason  from  the  particular  to  the  general,  instead  of  from 
all  the  parts  to  the  whole,  is,  we  believe,  the  fruitful  source  of 
this  class  of  invalid  judgments,  judgments  presented  as  premises 
for  the  deduction  of  conclusions. 

2.  Another  class  of  invalid  assumptions  is  this :  the  assump- 
tion that  a  mere  accident  is  an  essential  characteristic,  and 
hence  affirming  it  as  a  general  or  universal  characteristic  of  the 
individual  or  class  to  which  it  pertains.  One  substance  is  found, 
for  example,  in  certain  circumstances  combined  with  another. 
A  necessary,  and  consequent  universal  connection,  is  from 
hence  assumed.  Yet  the  connection,  in  the  circumstances  sup- 
posed, may  be  perfectly  accidental.  A.,  under  certain  provoca- 
tions, became  angry.  It  is  hence  assumed,  that  he  is  an  irrita- 
ble man.  Yret  his  general  character  may  be  the  total  opposite 
of  that  assumption.  The  error  here  described  really  falls  under 
that  first  stated.  It  is  presented  in  this  form,  for  the  sake  of 
distinctness.  * 

3.  Another  source  of  false  judgments  is  found  in  the  too 
common  practice  of  assuming  the  relation  of  invariable  or  uni- 
form sequence  from  mere  casual  coincidence,  and  of  cause  and 
effect  from  mere  accidental  antecedence  and  consequence.  Mere 
coincidence  does  not  authorize  the  assumption  of  a  necessary 
connection,  nor  mere  sequence  that  of  real  cause  and  effect. 
Yet  such  relations  are  quite  commonly  assumed  in  the  presence 
of  such  facts.     The  relation  of  cause  and  effect  can  be  properly 


assumed  but  in  vjew  of  the  fact  of  invariable  antecedence  and 
consequence.  This  is  the  lowest  condition  on  which  such  an 
assumption  can  be  aiithorized.  Another  condition  should  be 
uniformly  required — an  inability  to  account  for  the  connection 
referred  to,  on  any  other  supposition  than  the  relation  of  cause 
and  effect. 

4.  The  very  common  practice  of  assuming,  that  what  may 
be  true,  is  true,  is  another  fruitful  source  of  false  judgments. 
A.  may  have  acted  from  given  motives  in  such  and  such  circum- 
stances. From  hence  it  is  assumed,  that  he  did  then  act  from 
these  identical  motives.  Such  an  assumption  is  valid  but  upon 
one  supposition — that  no  other  motives  but  those  assigned  can 
originate  such  acts.  A  certain  class  of  facts  are  perceived  to 
consist  with  a  certain  hypothesis,  that  is,  it  is  perceived  that 
this  hypothesis  may  be  true.  It  is  hence  assumed  that  that  hy- 
pothesis is,  and  must  be,  true,  an  assumption  which  is  valid  but 
upon  one  condition — the  perception  that  these  facts  can  be  ex- 
plained on  no  other  supposition. 

5.  We  now  refer  to  another  equally  fruitful  source  of  false 
assumptions.  A  fact  or  class  of  facts,  equally  consistent  with 
two  or  more  distinct  and  opposite  hypotheses  is  assumed  as 
affirming  the  truth  of  one  in  opposition  to  that  of  the  others. 
It  is  a  universal  law  of  all  valid  intellectual  processes,  that  facts 
which  equally  consist  with  two  or  more  hypotheses,  prove 
neither  in  distinction  from  the  others.  Yet  such  facts  are  often 
made  the  basis  of  judgments,  that  one  hypothesis  is  true  and  all 
the  others  false.  The  same  error  is  very  common  in  the  cita- 
tion of  proof-texts  and  authorities.  No  judgment  is  affirmed 
by  any  facts  6*r  texts,  or  any  form  of  authority,  which  not  only 
does  not  affirm  the  truth  of  this  one  judgment,  but  in  reality 
denies  all  judgments  of  an  incompatible  or  opposite  nature. 

6.  Assuming  that  facts  which  are  equally  common  to  two 
classes  of  objects,  really  and  truly  pertain  to  one  class  in  dis- 
tinction from  the  other,  is  still  another  common  source  of  in- 
valid judgment.  Suppose  that  the  question  is,  Which  is  to  be 
preferred,  A  or  B  ?  Suppose  that  it  is  affirmed,  that  A  is  the 
fetter  of  the  i  wo.     The  reason  assigned  is,  that  the  element  C 


DOCTRINE     OF     FALLACIES.  229 

is  found  in  A.  Such  reason  has  real  weight  hut  upon  the  sup- 
position, that  C  is  of  decisive  value,  and  is  possessed  by  A,  and 
not  by  B.  If  it  belongs  to  each  alike,  it  presents  no  ground  for 
the  judgment,  "A  is  better  than  B."  Yet  the  form  of  false 
judgments  under  consideration  is  perfectly  common  in  the 
world,  and  not  uncommon  in  scientific  deduction. 

7.  Affirming  a  certainty,  when  the  facts  presented  authorize 
.only  the  assertion  of  a  probability \  is  still  another  common  form 
of  invalid  assumption.  How  often  do  we  hear  individuals  say- 
ing, "  I  felt  certain  that  the  case  was  so  and  so,  and  yet  I  found 
myself  mistaken."  A  recurrence  to  the  facts  known,  would 
show  clearly,  that  a  certainty  had  been  assumed,  when  only 
probability,  or  it  may  be,  a  bare  possibility,  was  truly  indicated. 

8.  Denying  the  manifest  bearing  and  fundamental  charac- 
teristics of  facts,  when  their  admission  would  contradict  some 
favorite  theory,  is  another  source  of  invalid  assumptions.  In 
such  cases,  which  often  occur,  not  only  in  common  life  but  even 
in  the  sphere  of  science,  we  have  nothing  but  assumption  in  op- 
position to  valid  evidence.  This  kind  of  assumption  involves  a 
violation  of  the  principle  of  sufficient  reason. 

9.  Refusing  to  place  facts  under  the  principle  or  class  to 
which  they  manifestly  belong,  and  arbitrarily  placing  them  un- 
der a  class  to  which  they  do  not  belong,  is  a  form  of  invalid 
assumption  which  we  often  meet  with.  Facts  are  often  pre- 
judged in  accordance  with  some  favorite  theory  or  assumption, 
and  then  obstinately  classed  accordingly.  Hence  the  best  ac- 
tions, for  example,  are  attributed  to  the  worst  motives,  and  vice 
versa  ;  and  all  this  by  an  arbitrary  act  of  will  or  assumption. 

10.  Assuming  that  facts  are  not  real  when  their  reality  is 
affirmed  by  valid  evidence,  or,  that  they  are  real  when  not  thus 
affirmed,  and  this  because  of  the  undeniable  bearing  of  the  facts 
granting  their  occurrence,  presents  forms  of  invalid  assumption, 
which  should  not  be  overlooked  in  this  connection.  No  degree 
of  evidence  can  induce,  in  some  instances,  the  admission  of  cer- 
tain facts,  and  any  form  of  evidence  will  be  readily  admitted 
for  the  occurrence  of  others.  The  reason  is  obvious.  The  lat- 
ter class  affirm  a  proposition,  the  truth  of  which  is  an  object  of 


230  LOGIC. 

strong  desire,  and  the  former  affirm  one,  the  admission  of  which 
is  an  object  of  corresponding  aversion.  We  find,  in  all  such 
cases,  nothing  but  assumption — assumption  opposed  to  valid 
evidence. 

11.  We  mention  another  additional  source  of  invalid  assump- 
tion :  assuming  that  a  mere  hypothesis,  consistent  throughout 
with  a  given  class  of  facts,  but  which,  for  aught  that  appears, 
may  or  may  not  be  true,  is  the  necessary  law  of  their  occur- 
rence. An  hypothesis  which  must  be  held  as  law,  not  only  con- 
sists with  the  class  of  facts  referred  to  it,  but  is  necessarily  sup- 
posed by  the  facts.  An  hypothesis  which  cannot  properly  be 
held  as  law,  though  consistent  with  the  facts,  may  or  may  not, 
for  aught  presented  in  them,  be  true.  There  may  be  classes  of 
facts,  and  there  are  many  such,  the  law  of  whose  existence,  and 
action  may  as  yet  be  wholly  unknown.  Suppose  that  an  hy- 
pothesis presents  itself,  an  hypothesis  consistent  with  all  that  is 
known  of  the  facts,  but  not  necessarily  supposed  by  them.  How 
readily  may  this  problematical  hypothesis  be  assumed  as  the 
ascertained  truth ! 

12.  Assumptions  which  violate  the  principles  of  identity  and 
contradiction  are  often  introduced  as  premises  into  processes  of 
reasoning,  or  presented  as  valid  in  themselves.  The  principle 
first  named  is  this :  that  "  conceptions  which  agree  can  in  thought 
be  united  or  affirmed  of  the  same  subject  at  the  same  time." 
The  second  is  this  :  "  The  same  attribute  cannot  be  at  the  same 
time  affirmed  and  denied  of  the  same  subject ;"  nor  can  incom- 
patible attributes  be  at  the  same  time  affirmed  of  the  same  sub- 
ject. The  principle  first  named  is  the  complement  of  the  latter. 
We  often  meet  with  judgments  which  violate  each  of  these  prin- 
ciples. Conceptions  which  agree  are  often  denied,  and  those 
which  disagree  are  as  often  affirmed,  of  each  other.  A.,  for  ex- 
ample, takes  the  life  of  B.,  under  circumstances  which  most 
manifestly  characterize  the  act  as  murder.  Yet  the  personal 
friends  of  A.  will  resolutely  refuse  to  place  the  act  under  the 
category  referred  to,  and  will  rank  it  under  an  opposite  one. 
A  characteristic  attaches  to  a  leading  dogma  of  a  particular  sect, 
a  characteristic  which  most  manifestly  marks  said  dogma  as  un- 


DOCTRINE   OF  FALLACIES.  231 

true,  or  self-contradictory  and  absurd.  Yet  every  member  of 
that  sect  will  refuse  to  place  that  dogma  under  such  category, 
and  as  arbitrarily  subsume  it  under  an  opposite  idea  or  princi- 
ple. A  mystery  is  often  rejected  as  an  absurdity  and  a  mani- 
fest absurdity  as  often  embraced  under  the  assumption,  that  it 
is  n  >t  an  absurdity  but  a  mystery.  In  all  such  cases  one  or  the 
other  of  the  principles  under  consideration  is  violated. 

13.  We  notice,  in  the  last  place,  a  class  of  assumptions  which 
violate  the  principle  of  implied  judgments — the  principle  that 
whatever  is  manifestly  implied  in  an  admitted  judgment,  must 
also  be  admitted.  In  opposition  to  this  principle,  judgments 
manifestly  implied  in  admitted  ones  are  often  denied,  and  the 
opposite  ones  assumed  as  true,  while  others  not  thus  implied  are 
assumed  as  implied.  In  all  theories  of  the  universe,  for  exam- 
ple, it  is  affirmed  that  creation  is  progressive  in  one  fixed  direc- 
tion— from  the  less  towards  the  more  perfect.  At  the  same 
time,  in  systems  of  skeptical  philosophy,  it  is  assumed  that  the 
order  of  nature  had  no  beginning,  but  is  self-subsisting  and  eter- 
nal. Now  progression  from  the  less  towards  the  more  perfect, 
necessarily  implies  a  commencement,  a  beginning  in  time.  Thus 
the  principle  of  implied  judgments  is  violated. 

In  the  above  classification  we  have  aimed  to  give  as  full  a  de- 
velopment of  the  sources  of  invalid  assumptions,  as  the  present 
state  of  scientific  investigation  will  permit.  That  some  of  such 
sources  may  have  been  overlooked,  is  most  probable.  What 
has  been  indicated,  however,  is  deemed  sufficient  to  give  a 
right  direction  to  the  investigations  of  the  inquirer  upon  this 
important  department  of  the  laws  of  thought,  and  also  to  pre- 
pare the  way  for  the  requisite  elucidation  of  the  department  of 
our  subject  next  in  order,  to  wit :  invalid  deductions  from  judg- 
ments assumed  as  true,  and  presented  as  the  basis  for  such  de- 
ductions. 

A  careful  investigation,  also,  of  the  above  classes  of  assump- 
tions, together  with  the  criteria  of  valid  judgments  given  in  the 
Analytic,  will  enable  the  inquirer  to  determine  what  judgments 
may  be  denied,  and  the  grounds  of  such  denial. 


CHAPTER  III. 

THE  DIALECTIC. 

Fallacies  in  Reasoning. 

It  now  remains  to  consider  the  third  and  last  source  of  falla- 
cies, to  wit :  that  which  especially,  hut  not  exclusively,  pertains 
to  the  connection  between  the  premises  and  conclusion  in  a  pro- 
cess of  reasoning.  In  examining  any  such  process,  three  dis- 
tinct inquiries  present  themselves:  the  validity  of  the  concep- 
tions themselves ;  that  of  judgments  laid  down  as  premises ; 
and  the  connection  between  said  premises  and  the  conclusions 
deduced  from  them.  In  every  valid  reasoning  process,  the  con- 
ceptions on  the  one  hand,  and  the  premises  on  the  other,  have 
all  the  characteristics  of  validity  developed  in  the  Analytic ;  and 
the  conclusion  in  accordance  with  laws  of  deduction  elucidated 
in  the  same,  necessarily  results  from  the  premises  from  which  it 
is  deduced.  In  every  invalid  process  there  is,  either  the  want 
of  the  characteristics  of  validity  referred  to  in  the  conceptions 
or  premises,  and  the  consequent  presence  in  one  or  both  of  the 
characteristics  of  invalidity  developed  in  the  preceding  chapters 
of  the  Dialectic,  or  a  want  of  valid  connection  between  the 
premises  and  the  conclusion,  or  the  presence  of  all  these  defi- 
ciencies in  the  same  process.  The  object  of  the  present  chapter 
is  to  develope  the  characteristics  of  one  source  of  fallacy  in  rea- 
soning— the  want  of  valid  connection  between  the  premises  and 
the  conclusion  deduced  from  them.  Other  sources  of  fallacy 
connected  with  this  will  also  be  developed.  The  inquirer  can- 
not be  too  often  reminded  of  the  fact,  that  it  is  perfectly  com- 
mon in  reasoning  to  lay  down  invalid  premises  as  the  basis  of 
conclusions,  and  of  the  consequent  necessity  of  rigidly  testing 
the  validity  both  of  premises  and  jf  the  conclusions  and  terms 
used.  Our  present  inquiries,  however,  lie  in  a  different  direc- 
tion, the  source  of  invalid  deductions. 


DOCTKINE     OF     FALLACIES 


GENERAL    CHARACTERISTICS    OF   ALL   INVALID    DEDUCTIONS. 

All  invalid  conclusions  are,  of  course,  either  assumed  a* 
proved  by  premises  which  prove  nothing,  which  fail  to  provt 
the  conclusion  deduced  from  them,  or  which  prove  not  this,  bul 
some  other  and  irrelevant  conclusion.  There  are  various 
forms  in  which  one  or  the  other  of  these  kinds  of  fallacy  appear 
We  will  notice  them  under  the  different  classes  above  stated. 


Section  I. — Conclusion^   deduced   from   Premises  which 

PROVE  NOTHING. 

It  would  hardly  be  expected,  that  even  intelligent  thinkers 
would  draw  inferences  from  premises  which  really  authorize  no 
conclusions  of  any  kind.  Such  facts,  however,  are  of  perfectly 
frequent  occurrence.     We  will  direct  attention  to  a  few  of  them. 

Arguing  from  tioo  Negative  or  two  Particular  Premises. 

One  of  the  most  obvious  forms  of  this  error  appears  when 
conclusions  are  deduced  from  two  negative  or  two  particular 
premises.  Such  premises,  as  we  have  already  seen,  authorize 
no  conclusions  whatever.  When  two  terms  are  excluded  from 
a  third,  which  is  true  where  we  have  two  negative  premises, 
nothing  whatever  can,  from  hence,  be  inferred  in  regard  to  the 
relations  of  the  terms  to  one  another.  When  we  have  two 
particular  premises,  one  extreme  may  be  compared  with  one 
part  of  the  middle  term,  and  the  other  with  another  part ;  so 
that  no  ground  for  an  inference  of  any  kind  is  present,  the  ex- 
tremes not  being  compared  with  the  same  thing.  Yet  we  fre- 
quently meet  with  precisely  such  deductions  as  these.  We  are 
often,  for  example,  met  with  the  inference,  that  two  entire 
classes  are  alike  or  unlike,  on  the  ground  that  some  individuals 
of  said  classes  agree  or  disagree  in  the  particulars  referred  to. 


Drawing  positive  conclusions  from  problematical 

The  common  practice  of  drawing  positive  inferences  from 
problematical  premises,  is  another  common  fallaey  which  belongs 
to  the  class  under  consideration.  A  problematical  judgment  is 
one  which  is  capable  of  being  proved  or  disproved,  and  needs 
proof.  Till  proved,  it  cannot  properly  be  employed  as  the  basis 
of  any  conclusions  of  any  kind.  Yet  it  is  perfectly  common  for 
individuals  to  lay  down  a  doubtful  proposition  and  one  really 
known  to  be  such,  as  presenting  an  ascertained  or  well-known 
truth,  and  then  make  use  of  such  proposition  as  the  basis  of  the 
conclusions  which  they  desire  to  reach.  A  problematical  propo- 
sition, it  should  be  borne  in  mind,  is  utterly  void  of  all  logical 
force.  It  authorizes  no  inferences  whatever.  This  error  in 
logic  is  one  form  of  the  so-called  petitio  principii,  or  begging 
the  question,  more  commonly  called  the  fallacy  of  undue  as- 
sumption. This  fallacy  most  frequently  occurs  in  this  form. 
Two  premises  are  laid  down,  which  together,  if  both  are  admit- 
ted, necessitate  the  conclusion  deduced  from  them ;  premises, 
one  of  which  is  admitted,  and  the  other  doubted  or  denied, 
while  both  alike  are  assumed  as  admitted.  Thus  the  conclu- 
sion is  begged  instead  of  proved,  no  conclusion  whatever  being 
authorized  by  the  premises  as  presented. 


Petitio  Principii. 

The  proper  petitio  principii,  however,  occurs  when  an  infer- 
ence is  deduced  from  a  proposition  which  is  really  identical  with 
the  inference  itself,  or  in  which  the  latter  is  directly  and  imme- 
diately implied.  While  the  conclusion  itself  is  problematical, 
the  same  must  be  true  of  every  judgment  identical  with  or  im- 
mediately implying  it.  The  former,  therefore,  is  utterly  void 
of  all  valid  logical  force,  and  to  argue  from  it  as  a  valid  basis  for 
inferences,  is  to  draw  conclusions  from  premises  which  pi-ove 
nothing.  Attempting  to  prove  the  being  of  God  from  the  tes- 
timony of  Scriptures  to  the  fact  of  his  being  and  perfections,  is 


DOCTRINE     OF     FALLACIES.  235 

an  example  of  this  kind,  the  conclusion  to  be  reached  being  im- 
plied in  the  premises  froni  which  it  is  deduced. 

Arguing  in  a  Circle. 

Arguing  in  a  circle,  that  is,  assuming  the  truth  of  the  conclu- 
sion from  the  assumption  that  the  premise  is  true,  and  then 
affirming  the  truth  of  the  latter  from  that  of  the  former,  is 
another  example  of  deduction  from  premises  which  prove 
nothing.  In  such  cases,  both  the  premise  and  the  conclusion 
are  in  turn  given  as  admitted  and  problematical  judgments. 
Neither,  therefore,  can  be-valid  as  the  basis  of  valid  deductions 
of  any  kind.  Arguing  the  authority  of  the  Church  from  the 
truth  and  divine  authority  of  the  Scriptures,  and  then  affirming 
the  latter  from  the  former,  is  an  obvious  and  commonly  adduced 
example  of  this  kind.  One  of  the  main  arguments  toJ  prove  the 
doctrine  of  necessity,  as  presented  by  some  of  our  ablest  and 
most  worthy  theological  metaphysicians,  is  another  very  striking 
example  of  this  kind.  The  will,  it  is  affirmed,  must  be  subject 
to  this  law,  because  its  determinations  are  always,  as  a  matter  of 
fact,  in  accordance  with  the  strongest  motive.  The  strongest 
motive  is  then  defined  to  be  that  to  which  said  determination 
is  conformed,  and  the  proof  that  this  motive  is  the  strongest  is 
affirmed  to  be  the  fact,  that  this  determination  is  conformed  to  it. 
If  this  motive  was  not  the  strongest,  it  is  replied,  the  will  would 
not  have  folloAved  it.  Now  here  are  the  three  logical  vices 
which  we  have  just  considered  :  reasoning  in  a  circle  ;  begging 
the  question  ;  and,  employing  as  a  premise  a  problematical,  in- 
stead of  an  ascertained,  judgment.  In  the  first  place,  the  truth 
of  the  doctrine  is  inferred  from  that  of  the  premise,  and  then, 
the  validity  of  the  premise  from  the  truth  of  the  doctrine.  The 
doctrine,  it  is  inferred,  is  true,  because  the  will  is  always  as  the 
strongest  motive,  "  the  greatest  apparent  good  ;"  and  then  the 
motive  which  the  will  does  follow  is  affirmed  to  be  the  strongest, 
because  the  will  must  follow  the  strongest  motive — that  is,  be- 
cause the  doctrine  first  deduced  from  the  assumed  validity  of 
the  premise  is  true.     Then  the  question  at  issue  is  begged  in 


the  assumption,  that  the  motive  to  which  the  will  conforms  its 
determinations  is  the  strongest.  This  assumption,  too,  is  used 
as  an  ascertained,  while  it  is,  in  fact,  nothing  but  a  problemati- 
cal, judgment. 


Deducing  positive  conclusions  from  Premises  known  to  be  in- 
valid in  t 


The  practice  of  deducing  conclusions  as  valid  from  premises, 
not  only  wanting  the  characteristics  of  validity  elucidated  in 
the  analytic,  but  possessing  the  positive  characteristics  of  inva- 
lidity  elucidated  in  the  dialectic  of  judgments,  should  not  be 
overlooked  in  this  connection. 

A  problematical  or  invalid  judgment  may  have  validity  as 
the  antecedent  or  consequent  of  a  conditional,  but  never  in  itself, 
nor  as  a  premise.  A  premise  void  of  the  characteristics  of  va- 
lidity or  possessed  of  those  of  an  opposite  character,  is  utterly 
void  of  all  valid  logical  force,  and  can  'authorize  no  inference 
whatever.  Yet  it  is  perfectly  common  for  premises  of  this  kind 
to  be  employed,  as  the  basis  of  the  most  important  conclusions, 
sometimes  ignorantly,  and  sometimes  intentionally.  One  of  the 
common  forms  of  this  fallacy  is,  to  ask  a  question  in  which  the 
false  judgment  is  tacitly  assumed  as  known  to  be  true,  and  so 
asked,  that  the  attention  is  diverted  from  this  assumption.  We 
have,  for  example,  seen  individuals  quite  embarrassed  by  the 
question,  "  Who  was  the  father  of  Zebedee's  children  ?"  Thus  * 
the  Royal  Society  was  imposed  upon  by  the  question,  "  How 
shall  the  fact  be  accounted  for,  that  a  vessel  of  water  receives 
no  addition  to  its  weight  when  a  live  fish  is  put  into  it  ?"  At- 
tention was  thus  directed,  by  the  form  of  the  question,  from  the 
fact  to  its  cause.  The  moment  attention  was  directed  from  the 
cause  to  the  fact,  the  false  assumption  was  corrected.  The  fal- 
lacy under  consideration  is  perhaps  of  most  frequent  occurrence 
in  this  form :  the  laying  down,  as  a  premise,  a  universal  propo- 
sition, when  only  a  particular  one  is  allowable,  and  then  de- 
ducing the  conclusion  which  the  former  would,  if  admitted,  au- 
thorize, instead  of  that  authorized  by  the  truly  allowable  one. 


DOCTEINE     OF     FALLACIES.  23? 

Hume's  celebrated  argument  against  miracles  is  of  this  char- 
acter. "  It  is  contrary  to  experience,"  he  says,  "  that  the  laws 
of  nature  should  be  suspended,  while  it  accords  with  experience 
that  testimony  should  prove  false.  Miracles,  therefore,  which 
imply  a  suspension  or  violation  of  the  laws  of  nature,  cannot  be 
established  by  testimony."  Now  the  minor  premise  being  that 
which  affirms,  that  it  accords  with  experience  that  testimony 
-should  prove  false,  is  unallowable  ;  because  its  contradictory — 
to  wit,  some  forms  of  testimony  never  prove  false — is  an  ascer- 
tained and  universally  admitted  truth.  The  Christian  syllogism 
upon  the  subject  is  this  :  some  kinds  of  testimony  never,  as  a 
matter  of  fact,  do  prove  false.  The  testimony  which  affirms  the 
truth  of  the  miracles  of  the  Bible  is  exclusively  of  this  charac- 
ter. The  major  premise  of  this  syllogism  none  will  dare  deny. 
Mr.  Hume,  then,  in  assuming  the  contradictory  of  this  as  true, 
has  laid  down  premises  which  prove  nothing  whatever.  His 
major  premise,  also,  is  unallowable  for  the  very  reason  that  the 
minor  is,  and  also  contains  the  fault  of  begging  the  question  at 
issue.  The  real  meaning  of  his  major  is  this  :  it  is  contrary  to 
universal  experience,  that  is,  to  the  experience  of  all  finite  in- 
telligences, that  the  laws  of  nature  should  be  suspended.  This, 
to  say  the  least,  is  not  an  ascertained  truth,  and  therefore  is 
utterly  void  of  all  logical  consequence  till  proven.  The  only 
major  that  he  was  authorized  to  lay  down,  was,  that  it  is  con- 
trary to  the  experience  of  some  men,  that  the  laws  of  nature 
should  be  violated  or  suspended.  In  using  the  universal  in- 
stead of  the  particular,  he  has  not  only  rendered  his  argument 
utterly  void  of  valid  logical  consequence,  but  has  begged  the 
whole  question  at  issue,  to  wit :  Whether  it  does  accord  with 
the  experience  of  some  individuals,  that  the  laws  of  nature 
should  be  suspended. 

We  might  adduce  other  examples  in  illustration  of  the  same 
principles.  These  are  sufficient,  however,  for  illustration,  and 
by  fixing  attention  upon  the  fact,  that  an  unallowable  premise 
is  void  of  all  logical  consequence,  to  induce,  as  we  hope,  the 
habit,  in  examining  processes  of  reasoning,  of  carefully  examin- 
ing the  character  and  validity  of  the  premises  laid  down.     The 


above  classes  of  fallacies,  also,  is  commonly  elucidated  under  the 
title  of  undue  assumption. 

Leap  in  Logic. 

What  is  called"  a  leap  (saltus)  in  logic  may  as  properly  be 
elucidated  in  this  connection  as  in  any  other,  as  it  falls,  in  fact, 
to  say  the  least,  under  the  principle  before  us.  Literally  there 
is  a  leap  in  logic,  when  the  conclusion  is  conjoined  with  one 
premise,  and  the  other  omitted.  This  may  always  be  legiti- 
mately done,  when  any  person  may  readily  supply  the  sup- 
pressed premise,  but  not  when  this  is  not  the  case.  The  fallacy 
which  goes  under  the  above  title  is  this :  A  conclusion  is  con- 
joined with  a  premise  with  which  it  has  a  very  remote,  and  no 
form  of  logical,  connection  at  all,  or  with  one  authorizing  no 
conclusion  of  any  kind.  And  all  this  under  the  assumption, 
that  the  suppressed  premise  legitimizes  said  connection.  The 
passage  across  the  chasm  which  really  separates  the  expressed 
premise  and  conclusion,  assumed  as  logically  resulting  from  it, 
is  called  a  leap  (saltus),  in  logic.  The  dogma  of  the  Romish 
Church,  that  because  Christ  gave  to  Peter  "  the  keys  of  the 
kingdom  of  heaven,"  that  therefore  his  assumed  successor  in 
Rome  holds  the  same,  is  a  striking  example  of  this  form  of  fal- 
lacy. The  syllogism  stated  in  full  is  this :  The  authority  con- 
ferred upon  Peter  vests  in  his  assumed  successor  in  Rome  ;  the 
present  pope  is  such  successor ;  therefore,  the  authority  con- 
ferred upon  Peter  vests  in  said  pope.  Any  one  can  see,  in  a 
moment,  that  the  major  premise  here  is  totally  void  of  all  va- 
lidity. There  is  not  a  shadow  of  evidence  anywhere  of  its  truth. 
On  the  other  hand,  we  have  the  most  positive  evidence  of  its 
invalidity.  The  language  of  Christ  to  Peter  is  exclusively  per- 
gonal and  applicable  to  him  alone :  "  I  give  to  thee  the  keys," 
&c. ;  "  Whatsoever  thou  shalt  bind  on  earth,"  &c.  Where  is 
the  foundation  for  the  inference,  that  what  was  thus  conferred 
upon  Peter  vests  in  his  assumed  successor?  We  will  give 
another  example  of  the  fallacy  before  us — an  example  from  the 
productions  of  modern  infidelity :  "Of  the  origin  of  the  Booka 


DOCTRINE     OF     FALLACIES.  239 

of  Moses,"  says  Prof.  Robert  Hare,  of  Philadelphia,  "  no  higher 
evidence  exists,  according  to  the  testimony  of  the  Bible  itself, 
than  that  of  an  obscure  priest  and  a  fanatical  king."  What 
evidence  is  adduced  by  this  author  to  sustain  this  broad  and 
sweeping  assertion  ?  Simply  the  following  statement  found  in 
the  24th  chap,  of  2  Chronicles  and  the  22d  of  2  Kings:  "And 
when  they  brought  out  the  money  that  was  brought  into  the 
house  of  the  Lord,  Hilkiah  the  priest  found  a  book  of  the  law 
of  the  Lord  given  by  Moses,"  together  with  the  subsequent 
statement  that  "Hilkiah  delivered  the  book  to  Shaphan," 
"  and  Shaphan  read  it  before  the  king ;"  and  finally,  that  the 
king  subsequently  "  read*to  all  the  men  of  Judea  and  the  in- 
habitants of  Jerusalem,"  &c,  "  all  the  words  of  the  book  of  the 
covenant  that  was  found  in  the  house  of  the  Lord."  After 
citing  the  account  given  by  Josephus  of  the  same  facts,  an  ac- 
count identical,  in  all  respects,  with  that  given  in  the  chapters 
referred  to,  with  the  exception,  that  Josephus  states  what  is  not 
affirmed  in  these  chapters,  nor  implied  in  any  of  its  statements, 
that  all  of  the  "  sacred  Books  of  Moses"  were  found  at  that  time, 
our  author  makes  the  following  statement :  "  If  the  Pentateuch 
had  been  previously  known  to  the  Jews,  it  is  incredible  that  it 
could  have  become  obsolete  and  forgotten  prior  to  the  alleged 
discovery  of  it  in  the  temple  in  the  reign  of  Josiah."  From 
these  simple  statements  the  Professor  deduces  such  conclusions 
as  the  following  :  1.  The  books  here  found  were  all  the  Books 
of  Moses.  2.  These  entire  writings  were,  and  had  been,  up 
to  that  time  wholly  unknown  to  the  whole  Jewish  nation. 
3.  Moses  never  wrote  these  books.  4.  They  are  gross  forgeries 
palmed  upon  the  nation  and  the  world  by  this  "  obscure  priest 
and  fanatical  king,"  &o.  Now  what  a  leap  in  logic  is  here. 
Not  one  of  the  conclusions  has  the  remotest  connection  with 
the  facts  adduced  to  prove  them.  For  aught  that  appears  in 
the  Bible,  but  one  of  the  five  books  of  Moses  was  then  found ; 
and  for  aught  that  appears  or  is  implied  in  the  facts  stated,  mul- 
titudes of  copies  might  have  existed  among  the  ten  tribes  then 
in  captivity,  and  even  in  Judea  itself.  The  fact,  that  a  copy  of 
these  writings  was  found  in  this  place,  and  that  the  king  was 


240  LOGIC. 

deeply  moved  by  the  parts  subsequently  read  to  him,  affords 
not  the  shadow  of  evidence  that  these  writings  were  utterly  un- 
known to  all  the  tribes  of  that  nation,  and  that  no  other  copies 
then  existed  among  them.  Then  the  universal  reception  of 
these  writings,  not  only  by  the  individuals  of  Judea,  but  also 
by  the  hostile  tribes  then  in  captivity,  shows  clearly  that  these 
writings  could  not  have  been  unknown  to  the  nation. 

Proving  too  much. 

Sometimes  a  premise  is  laid  down  with  which  the  conclusion 
sought  has  a  necessary  connection,  but  with  which,  also,  a  con- 
clusion, known  to  be  false,  has  a  connection  equally  necessary. 
In  such  a  case  the  argument  is  said  to  prove  too  much,  and  in 
doing  so,  to  prove,  not  the  conclusion  sought  to  be  established 
by  it,  but  its  own  utter  invalidity  as  the  basis  of  any  valid  con- 
clusion whatever ;  for  a  proposition  connected  by  necessary  an- 
tecedence with  a  consequent  known  to  be  false,  must  itself  be 
false,  and  therefore  utterly  void  of  all  valid  logical  consequence. 
If,  for  example,  an  individual  should  adduce  the  infinity  and 
perfection  of  Deity,  as  proof  of  the  non-perpetuity  of  moral  and 
physical  evil  in  the  universe,  the  proper  reply  would  be,  that 
this  argument  proves  too  much,  being  equally  conclusive  against 
the  present  as  well  as  perpetual  existence  of  these  evils,  while 
their  present  existence  is  a  known  fact.  That  which  now  exists, 
notwithstanding  the  attributes  referred  to,  may,  for  aught  that 
can  be  deduced  from  the  same,  exist  forever. 

Inferring  the  falsity  of  the  conclusion  from  that  of  thepremise, 
or  the  truth  of  the  premise  from  the  truth  of  the  conclusion. 

As  belonging  to  the  same  general  class  under  consideration, 
we  now  refer  to  the  very  common  error  of  inferring  the  falsity 
of  the  conclusion  from  that  of  the  premise,  and  the  truth  of  the 
former  from  that  of  the  latter.  To  prove  a  proposition  false  is, 
as  we  have  already  shown,  to  show  that  it  is,  as  a  premise,  void 
of  all  valid  logical  consequence.     We  have  not  thereby  touched 


DOCTRINE     OF     FALLACIES.  241 

the  question,  whether  the  conclusion  deduced  from  it  is  in  itself 
true  or  false,  any  more  than  we  have  determined  the  character 
of  the  consequent  in  a  conditional  proposition,  when  we  have 
merely  denied  the  antecedent. 

So  when  we  have  admitted  a  conclusion  deduced  from  certain 
premises,  and  admitted  it  as  true  in  itself,  we  have  thus  deter- 
termined  nothing  whatever  relatively  to  the  truth  or  falsity  of 
the  premise  itself,  any  more  than  the  admission  of  the  conse- 
quent determines  the  truth  or  falsity  of  the  antecedent  in  a  con- 
ditional judgment.  Yet  no  forms  of  fallacy  are  more  common 
than  the  two  now  under  consideration,  and  from  this  fact  two 
evils  of  very  great  magnitifde  arise — to  wit,  that  by  unsound 
arguments  adduced  in  support  of  truth,  truth  itself  is  often  be- 
trayed into  the  hands  of  its  enemies ;  and  that  the  most  obvious 
and  important  truths  are  so  often  defended  by  invalid  argu- 
ments. When  the  truth  of  any  given  doctrine  or  principle  is 
very  obvious,  its  advocates  are  very  apt  to  assume  that  any 
form  of  argument  for  its  truth  must  be  valid,  and  for  this  rea- 
son to  defend  it  with  very  feeble  and  even  unsound  arguments ; 
while  the  refutation  of  such  arguments  induces  a  doubt  of  the 
truth  itself. 


Fallacy  of  References. 

There  is  still  another  form  of  fallacy  falling  under  the  present 
division  of  our  subject,  a  fallacy  quite  common  in  theological 
writings  especially,  that  of  references,  which  is  set  forth  with 
much  distinctness  by  the  following  extract  from  Dr.  Whately  : 
I  It  is,  of  course,  a  circumstance  which  adds  great  weight  to  any 
assertion,  that  it  shall  seem  to  be  supported  by  many  passages 
of  Scripture  ;  now  when  a  writer  can  find  few  or  none  of  these 

.  that  distinctly  and  decidedly  favor  his  opinion,  he  may  at  least 
find  many  which  may  be  conceived  capable  of  being  so  under- 
stood, or  which,  in  some  way  or  other,  remotely  relate  to  the 
subject ;  but  if  these  texts  were  inserted  at  length,  it  would  be 

I  at  once  perceived  how  little  they  bear  on  the  question :  the 

usual  artifice,  therefore,  is,  to  give  merely  references  to  them, 

11 


trusting  that  nineteen  out  of  twenty  readers,  will  never  take  the 
trouble  of  turning  to  the  passages,  hut,  taking  for  granted  that 
they  afford,  each,  some  degree  of  confirmation  to  what  is  main- 
tained, will  he  overawed  by  seeing  every  assertion  supported, 
as  they  suppose,  by  five  or  six  Scripture-texts."  References 
however  numerous,  it  should  be  borne  in  mind,  prove  nothing 
whatever  unless  they  are  to  the  point ;  and  if  they  are  to  the 
point,  one,  as  far  as  real  proof  is  concerned,  is  as  good  as  a 
thousand. 

Fallacies  connected  with  the  use  of  the  Middle  Term. 

We  now  refer  to  another  class  of  fallacies,  which  should  be 
treated  of  in  the  present  connection — those  which  arise  from  an 
illogical  use  of  the  middle  term.  Among  these  we  notice  the 
following  classes : 

1.  The  undistributed  middle. — Premises  in  which  the  middle 
term  is  not  distributed  are,  as  we  have  before  shown,  void  ut- 
terly of  all  logical  consequence.  When  any  conclusion  is  de- 
duced from  such  premises,  it  is  deduced  from  premises  which 
authorize  no  conclusion  whatever. 

The  form  in  which  this  fallacy  most  commonly  appears,  is 
when  the  middle  term,  as  the  subject  of  a  proposition  really 
particular,  is  used  without  any  qualifying  terms,  which  imply 
distribution  or  non-distribution,  and  when,  consequently,  it  will 
be  likely  to  be  understood  as  distributed  when  it  is  not.  For 
example : 

Food  is  necessary  to  life.; 

This  article  is  food  ; 

Therefore,  it  is  necessary  to  life. 

The  fact  of  non-distribution  is  most  likely  not  to  be  noticed, 
when  the  fact  stated  is  generally,  though  not  universally,  true 
of  the  whole  class  referred  to. 

2.  The  ambiguous  middle— -This  fallacy  consists  in  employ- 
ing as  a  middle  term  a  word  or  phrase  which  has  two  significa- 
tions, and  employing  it  in  one  sense  in  one  premise,  and  in 
another  in  the  other ;  while  in  the  conclusion  the  extremes,  on 


DOCTKINE      OF     FALLACIES.  243 

account  of  their  relations  to  the  middle,  are  affirmed  to  agree 
or  disagree  with  each  other,  as  the  case  may  be.  In  seme  in- 
stances the  word  or  phrase  may  be  ambiguous  in  itself.  Thus 
the  term  "know"  sometimes  means  a  mere  intellectual  appre- 
hension, as  in  the  Bible  statement,  "When  they  knew  God, 
they  glorified  him  not  as  God ;"  or  such  apprehension  accom- 
panied with  a  corresponding  state  of  the  heart  or  internal  expe- 
rience, as  in  the  phrase,  "And  this  is  life  eternal,  that  they 
might  know  thee,  the  only  true  God,  and  Jesus  Christ,  whom 
thou  hast  sent."  A  proposition  might  be  true  or  false  accord- 
ing to  the  special  sense  in  which  it  is  employed  in  any  given 
case.  If  any  such  term  is  employed  in  one  sense  in  one  premise, 
and  in  another  in  the  other,  then  we  have  really  two  middle 
terms  instead  of  one,  and  the  extremes  are  not  at  all  compared 
with  the  same  thing.  "  It  is  worth  observing,"  says  Dr.  Whate- 
ly,  "that  the  words  whose  ambiguity  is 'the  most  frequently 
overlooked,  and  is  productive  of  the  greatest  amount  of  confu- 
sion of  thought  and  fallacy,  are  among  the  commonest,  and  are 
those  of  whose  meaning  the  generality  consider  there  is  the 
least  room  to  doubt.  It  is,  indeed,  from  these  very  circum- 
stances that  the  danger  arises  ;  words  in  very  common  use  are 
both  the  most  liable,  from  the  looseness  of  ordinary  discourse, 
to  slide  from  one  sense  into  another,  nwl  also  the  least  likely  to 
have  that  ambiguity  suspected." 

The  middle  term  may  also  be  ambiguous  for  J.  3  reason  thut 
it  is  employed  in  one  premise  distributive^,  ixnii  m  th-,  other 
collectively.  This  is  called  the  fallacy  of  divis»or  vtuk  'ytznpo** 
tion.     For  example : 

Five  is  one  number  ; 
Three  and  two  are  five  ; 
.•.  Three  and  two  are  one  number. 

Three  and  two  are  two  numbers  ; 
Five  is  three  and  two  ; 
.•.  Five  is  two  numbers. 

The  first  of  the  above  examples  belongs  to  what  is  called 
"fallacy  of  division,"  and  the  second  to  those  of  composition. 


Any  one  will  perceive,  on  reflection,  that  in  the  second  premise 
of  the  first  example,  the  phrase  "  three  and  two"  is  taken  col- 
lectively, and  means,  that  taken  together,  these  numbers  are 
equal  in  quantil  y  to  the  number  five  ;  while  in  the  conclusion 
the  same  phrase  is  taken  distributively,  the  meaning  being,  that 
"  three  and  two,"  -as  an  inferior,  rank  under  the  superior  con- 
ception represented  by  the  words  "  one  number."  Similar  re- 
marks are  applicable  to  the  second  example. 

This  form  of  fallacy  is  so  well  elucidated  by  Dr.  Whately, 
that  we  will  conclude  what  we  have  to  say  upon  it  with  the  fol- 
lowing lengthy  extract  from  him  : 

"  To  this  head  may  be  referred  the  fallacy  by  which  men 
have  sometimes  been  led  to  admit,  or  pretend  to  admit,  the 
doctrine  of  necessity :  e.  g.  '  he  who  necessarily  goes  or  staya 
(i.  e.  in  reality,  '  who  necessarily  goes  or  who  necessarily  stays') 
is  not  a  free  agent ;  you  must  necessarily  go  or  stay  (i.  e.  '  you 
must  necessarily  take  the  alternative'')  ;  therefore,  you  are  not  a 
free  agent.'  Such,  also,  is  the  fallacy  which  probably  operates 
on  most  adventurers  in  lotteries :  e.  g.  '  the  gaining  of  a  high 
prize  is  no  uncommon  occurrence ;  and  what  is  no  uncommon 
occurrence  may  reasonably  be  expected  ;  therefore,  the  gaining 
of  a  high  prize  may  reasonably  be  expected :'  the  conclusion, 
when  applied  to  the  individual  (as  in  practice  it  is),  must  be  un- 
derstood in  the  sense  of '  reasonably  expected  by  a  certain  indi- 
vidual /'  therefore,  for  the  major  premise  to  be  true,  the  mid- 
dle term  must  be  understood  to  mean,  '  no  uncommon  occur- 
rence to  some  one  particular  person  ;'  whereas  for  the  mmor 
(which  has  been  placed  first)  to  be  true,  you  must  understand 
it  of  'no  uncommon  occurrence  to  some  one  or  other f  and 
thus  you  will  have  the  fallacy  of  composition." 

There  is  no  fallacy  more  common,  or  more  likely  to  deceive, 
than  the  one  now  before  us ;  the  form  in  which  it  is  most  usual- 
ly employed  is,  to  establish  some  truth  separately  concerning 
each  single  member  of  a  certain  class,  and  thence  to  infer  the 
same  of  the  whole  collectively :  thus  some  infidels  have  labored 
to  prove  concerning  some  one  of  our  Lord's  miracles,  that  it 
niight  have  been  the  result  of  an  accidental  conjunction  of  natu- 


DOCTRINE     OF     FALLACIES.  245 

ral  circumstances ;  next  they  endeavor  to  prove  the  same  con- 
cerning another  •  and  so  on  ;  and  thence  infer  that  all  of  them 
might  have  been  so.  They  might  argue,  in  like  manner,  that 
because  it  is  not  very  improbable  one  may  throw  sixes  in  any 
one  out  of  a  hundred  throws,  therefore  it  is  no  more  improba- 
ble that  one  may  throw  sixes  a  hundred  times  running. 

This  fallacy  may  often  be  considered  as  turning  on  the  ambi- 
guity of  the  word  "  all ;"  which  may  easily  be  dispelled  by  sub- 
stituting for  it  the  word  "  each"  or  "  every,"  where  that  is  its 
signification :  e.  g.  "  All  these  trees  make  a  thick  shade,"  is 
ambiguous,  meaning,  either  "  every  one  of  them,"  or  "  all  to- 
gether." 

This  is  a  fallacy  with  which  men  are  extremely  apt  to  deceive 
themselves  ;  for  when  a  multitude  of  particulars  are  presented 
to  the  mind,  many  are  too  weak  or  too  indolent  to  take  a  com- 
prehensive view  of  them ;  but  confine  their  attention  to  each 
single  point  by  turns ;  and  then  decide,  infer,  and  act,  accord- 
ingly :  e.  g.  "  The  imprudent  spendthrift,  finding  that  he  is  able 
to  afford  this,  or  that,  or  the  other,  expense,  forgets  that  all  of 
them  togetJier  will  ruin  him." 

To  the  same  head  may  be  reduced  that  fallacious  reasoning, 
by  which  men  vindicate  themselves  to  their  own  conscience 
and  to  others,  for  the  neglect  of  those  undefined  duties,  which, 
though  indispensable,  and  therefore  not  left  to  our  choice 
whether  we  will  practise  them  or  not,  are  to  our  discretion  as 
to  the  mode  and  the  particular  occasions  of  practising  them : 
e.  g.  "  I  am  not  bound  to  contribute  to  this  charity  in  particu- 
lar ;  nor  to  that ;  nor  to  the  other."  The  practical  conclusion 
which  they  draw  is,  that  all  charity  may  be  dispensed  with. 

As  men  are  apt  to  forget  that  any  two  circumstances  (not 
,  naturally  connected)  are  more  rarely  to  be  met  with  combined 
than  separate,  though  they  be  not  at  all  incompatible  ;  so  also 
they  are  apt  to  imagine,  from  finding  that  they  are  rarely  com- 
bined, that  there  is  an  incompatibility :  e.  g.  "  If  the  chances 
are  ten  to  one  against  a  man's  possessing  strong  reasoning 
powers,  and  ten  to  one  against  exquisite  taste,  the  chances 
against  the  combination  of  the  two  (supposing  them  neither 


246  LOGIC. 

connected  nor  opposed)  will  be  a  h  mdred  to  one."  Many, 
therefore,  from  finding  them  so  rarely  united,  will  infer  that 
they  are  in  some  measure  incompatible ;  which  fallacy  may 
easily  be  exposed  in  the  form  of  the  undistributed  middle : 
"  Qualities  unfriendly  to  each  other  are  rarely  combined ;  ex- 
cellence in  the  reasoning  powers  and  in  taste  are  rarely  com- 
bined ;  therefore,  they  are  qualities  unfriendly  to  each  other." 

The  argument  for  the  Divine  Infinity  drawn  from  the  mere 
extent  of  creation,  is  a  very  striking  example  of  this  form  of  fal- 
lacy. It  is  self-evident,  that  the  element  of  real  infinity  in  the 
cause  cannot  be  logically  deduced  from  the  mere  element  of 
extent  in  the  effect,  when  that  effect,  however  vast,  is  known 
to  be  of  finite  or  limited  extent.  Nothing  can  endanger  the 
ultimate  effect  of  the  theistic  argument  so  much  as  to  base  such 
a  conclusion  upon  such  premises.  Equally  fatal  and  fallacious 
is  the  assumption,  that  if  this  element  in  creation  does  not  afford 
a  basis  for  such  a  conclusion,  none  other  does  exist.  To  us  it  is, 
d  priori,  certain,  that  if  God  has  penciled  out  the  evidence  of  • 
his  own  absolute  infinity  and  perfection  somewhere  upon  the 
works  of  his  hands,  and  no  one  will  say  that  he  cannot  do  it, 
and  has  not  done  it,  those  pencillings  are  to  be  found,  not  in 
the  combinations  of  matter,  but  in  the  laws,  principles,  and  sus- 
ceptibilities of  that  which  is  created  in  the  Divine  image  ;  and 
here,  Ave  affirm,  those  pencillings  are  found.  This,  however,  is 
not  the  place  to  present  the  proof  of  this  statement. 

3.  Fallacy  of  accidents — Fallacia  accidentia. — The  fallacy 
which  next  claims  our  attention  as  connected  with  the  middle 
term,  is  denominated  "  the  fallacy  of  accidents,"  and  consists  in 
employing  the  middle  term  in  one  premise  to  represent  some- 
thing considered  in  itself  as  to  its  real  essence  exclusively,  and 
in  the  other  to  represent  this  in  connection  with  its  accidents  of 
time,  place,  or  changes,  &c.  The  well-known  example,  "  What  ' 
is  bought  in  the  market  is  eaten ;  raw  meat  is  bought  in  the 
market ;  therefore,  raw  meat  is  eaten,"  is  commonly  given  in 
illustration  of  this  fallacy,  and  well  illustrates  it. 

4.  Akin  to  the  above  is  the  "  fallacy  of  quid,"  which  consists 
in  employing  the  middle  term  in  its  widest  acceptation  in  one 


DOCTRINE      OF     FALLACIES.  247 

premise,  and  in  reference  to  its  special  applications  in  the  other. 
Thus  the  term  "  innocent"  may  be  employed  to  signify  univer- 
sal freedom  from  moral  faults  of  any  kind,  or  freedom  from 
some  particular  fault  with  which  an  individual  stands  charged 
at  some  particular  time.  Suppose  that  in  the  two  premises  of  a 
given  syllogism,  this  term  is  employed  in  these  two  distinct  and 
opposite  senses.  We  should  then  have  an  example  of  the  fal- 
•  lacy  of  very  frequent  occurrence. 


CONDITIONAL    SYLLOGISMS    WHOSE    CONDITIONAL    PREMISES    ARE 
VOID    OF  LOGICAL   CONSEQUENCE. 

One  of  the  most  common  forms  of  fallacy  falling  under  the 
class  we  are  now  considering  is,  the  employment  of  that  form 
of  the  conditional  syllogism  in  which  the  conditional  premise  is 
void  of  all  logical  consequence.  The  validity  of  the  conditional 
syllogism  is  conditioned  wholly  upon  the  relation  of  necessary 
consequence  between  the  antecedent  and  consequent  in  the  ma- 
jor premise.  Where  this  relation  does  not  obtain,  this  premise 
is  wholly  void  of  all  logical  consequence,  and  the  conclusion 
resting  upon  it  is  without  any  valid  foundation.  Take  as  an 
illustration  the  common  example  :  "  If  Cromwell  was  an  Eng- 
lishman he  was  a  usurper  ;  he  was  an  Englishman  ;  therefore, 
he  was  a  usurper."  When  we  examine  the  hypothetical 
premise  in  this  case,  we  find  that  there  is  no  relation  what- 
ever of  logical  consequence  between  the  antecedent  and  con- 
sequent. The  premises,  therefore,  prove  nothing.  In  such  a 
palpable  case  no  one  would  be  deceived  by  the  argument  pre- 
sented. Cases,  however,  often  occur  in  which  the  error  is  less 
likely  to  be  detected,  than  in  almost  any  other  instances  of  fal- 
lacious reasoning.  Suppose  that  an  individual  has  a  bad  cause 
to  advocate.  He  commences  by  saying  that  "  if  he  succeeds 
in  establishing  such  and  such  propositions,  every  one  will  grant 
that  he  has  proven  the  conclusion  which  he  was  called  upon  to 
establish."  In  such  circumstances,  the  attention  of  the  listener 
is  very  likely  to  be  turned  from  a  consideration  of  the  relation 
of  consequence   between   the   antecedent  and   consequent,  to 


that  of  fact ;  that  is,  whether  the  individual  does,  or  does  not, 
prove  the  propositions  referred  to.  If,  in  addition  to  this,  he 
can  induce  his  opponent  to  join  issue  with  him,  not  in  reference 
to  the  relation  referred  to,  hut  in  respect  simply  to  the  question 
of  fact,  then  the  fallacy  is  almost  certain  not  to  he  detected. 

How  often  do  individuals,  in  replying  to  a  sophistical  argu- 
ment, err  here.  They  do  not  turn  attention  to  the  want  of 
logical  consequence  under  consideration,  hut  join  issue  relative- 
ly to  the  question  of  fact,  the  very  point  prohably  where  the 
sophist  is  the  strongest,  and  where,  if  the  position  he  claims 
should  be  granted,  it  is  perfectly  impossible  to  show  that  the 
conclusion  he  deduces  is  not  reached. 


DISJUNCTIVE     SYLLOGISMS     WHOSE     DISJUNCTIVE    PREMISES     ARE 
VOID    OF   LOGICAL   CONSEQUENCE. 

Similar  fallacies  are  often  connected  with  the  disjunctive  syl- 
logism. The  disjunctive  premise,  to  be  valid,  must,  as  we  have 
seen,  embrace  all  conceivable  or  possible  hypotheses  falling, 
within  the  sphere  of  the  disjunction ;  else  it  is  void  of  conse- 
quence. Suppose,  for  example,  we  have  the  following  disjunc- 
tive syllogism : 

A  is  in  B,  C,  D,  or  E  ; 
It  is  not  in  B,  C,  or  D  ; 
.-.  It  is  in  E. 

All  that  is  requisite  to  annihilate  totally  the  validity  of  this  ar- 
gument, is  to  show  that  A  may  be  in  F  instead  of  E.  In  that 
case,  when  we  grant  the  truth  of  the  minor  premise,  we  do  not 
grant  that  of  the  conclusion. 

We  will  give  an  example  of  the  fallacy  of  which  we  are 
speaking.  It  is  found  in  the  celebrated  statement  of  Kant  rela- 
tively to  the  possible  proofs  of  the  being  of  God.  We  will  give 
the  statement  in  the  words  of  the  author  himself : 

"  There  cannot  be  but  three  sorts  of  proof  of  the  existence  of 
God  from  speculative  reason  :  The  physico-theological,  in  which 
we  begin  with  the  determinate  experience,  and  the  thereby 
known  peculiar  quality  of  our  sensible  world,  and  mount  from 


DOCTRINE     OF     FALLACIES.  249 

it,  according  to  laws  of  causation,  to  the  very  Supreme  Cause 
out  of  the  world  ;  the  cosmological,  in  which  we  lay  indetermi- 
nate experience  only,  that  is,  any  one  existence  empirically  as  a 
ground  ;  and  the  ontological,  in  which  we  abstract  from  all  ex- 
perience, and  from  mere  conceptions  infer  the  existence  of  a 
Supreme  Cause  quite  d  priori." 

"The  cosmological  proof,"  in  the  language  of  the  author 
himself,  "  runs  thus :  If  something  exists,  an  absolutely  neces- 
sary being  must  exist ;  now  I,  at  least,  exist  myself;  therefore, 
an  absolutely  necessary  being  exists."  In  reply  to  this  argu- 
ment it  is  enough  to  say,  that  it  determines  nothing  specific  in 
regard  to  the  character  of  this  necessary  being,  and  is  thus  void 
of  logical  validity  when  adduced  as  proof  of  the  existence  of 
God,  that  is,  of  a  necessary  being  of  absolute  infinity  and  per- 
fection. 

The  ontological  argument  concludes  from  the  fact,  that  there 
is  in  the  human  mind  the  conception  of  such  a  being,  that  such 
a  being  exists.  This  argument  fails  for  this  reason — that  it  is 
really  based  upon  the  assumption,  that  the  existence  in  the  in- 
telligence of  a  conception  is  proof  of  the  existence  of  a  corre- 
sponding object,  which  is  by  no  means  true.  The  argument, 
therefore,  is  invalid. 

"  The  main  points  of  the  physico-theological  proof,"  in  the 
language  of  our  author,  "are  as  follows :  1.  Everywhere  in  the 
wrorld  there  are  distinct  marks  of  an  arrangement  according  to 
a  determinate  design  executed  with  great  wisdom,  and  in  a 
whole  of  indescribable  variety,  as  well  as  of  unbounded  great- 
ness of  sphere.  2.  This  arrangement,  so  answerable  to  the  end, 
is  quite  foreign  to  the  things  of  the  world,  and  adheres  to  them 
fortuitously  only ;  that  is,  the  nature  of  the  different  things 
could  not  agree  of  its  own  accord  in  determinate  designs  by  so 
various  uniting  means,  were  it  not  chosen  and  disposed  for  that 
purpose  entirely  by  a  rational  Principle  ordering  it  according 
to  ideas  laid  as  a  foundation.  3.  Therefore  there  exists  a  sub- 
lime and  a  wise  Cause  (or  more  of  them),  which  must  be  that 
of  the  world,  not  only  as  blind,  working  all-powerful  nature  by 
fertility,  but  as  an  Intelligence,  by  liberty.      4.  This  Cause's 


250  LOGIC. 

unity  may  be  inferred,  from  the  unity  of  the  reciprocal  reference 
of  the  parts  of  the  world,  as  members  of  an  artificial  structure, 
in  that  to  which  our  observation  reaches,  Avith  certainty,  but 
further,  on  all  the  principles  of  analogy,  with  probability." 

To  this  argument  Kant  replies,  that  admitting  its  validity,  as 
far  as  it  goes,  there  is  an  infinite  chasm  between  the  inference 
which  it  does  yield  and  the  conclusion  demanded  by  theism,  to 
wit,  that  the  Cause  under  consideration  is  a  being  of  absolute 
infinity  and  perfection.  The  universe  being  finite  in  extent, 
cannot,  by  its  extent,  give  proof  of  the  actual  infinity  of  its 
author.  An  argument  Avhich  falls  short  of  proving  the  being 
of  God  as  infinite  and  perfect,  fails  wholly  to  prove  the  being  of 
God.  Thus  it  is  that  each  of  the  only  possible  arguments  for 
the  being  of  God  fails  of  its  end,  and  we  are  left  without  such 
proof.     The  real  syllogism  of  Kant  may  be  thus  presented  : 

The  proof  of  the  being  and  perfections  of  God  is  found  in  one 
of  the  three  forms  of  argument  above  named,  or  we  have  no 
such  proof.  That  proof  is  not  contained  in  these  arguments. 
Therefore,  we  have  no  logically  valid  proof  of  the  Divine  exist- 
ence. In  reply,  we  remark,  that  the  above  argument,  even 
as  presented  by  Kant  himself,  does  afford  the  following  valid 
conclusions:  1.  The  actual  existence  of  a  necessary  being  of 
some  character.  2.  This  being  is  a  free,  intelligent,  self-con- 
scious personality,  endowed  with  attributes  inconceivably  great, 
sublime,  and  incomprehensible.  3.  There  is  the  total  absence 
of  all  evidence,  that  this  being  is  not  infinite  and  perfect.  The 
error  of  Kant  consists  in  the  assumption,  that  no  form  of  evi- 
dence exists  of  the  infinity  and  perfection  of  this  Being,  whose 
existence  is  thus  demonstrated,  but  what  is  yielded  by  the  mere 
extent  of  creation.  We  say  that  it  is  not,  d  priori,  certain  that 
God  cannot,  and  has  not,  in  a  creation  of  finite  extent,  pencilled  - 
out  absolute  indications  of  his  own  infinity  and  perfection. 
There  may  be  other  elements  of  proof  bearing  upon  this  sub- 
ject than  that  of  mere  extent  in  creation.  The  laws  of  mind 
may  yield  absolute  proof  of  the  absolute  infinity  and  perfection 
of  this  Being.  No  one  can  affirm,  d  priori,  that  this  is  not  the 
case.     Kant  decides  wholly,  d  prioi'i,  that  all  the  proof  bear- 


DOCTRINE     OF     FALLACIES.  251 

ing  upon  this  question  is  found  in  the  three  forms  of  argument 
which  he  has  presented.  We  reply,  that  there  may  he  another 
source  of  proof  of  equal  validity,  which  this  author  has  wholly 
omitted.  His  syllogism,  therefore,  is  utterly  void  of  logical  va- 
lidity. 

FALLACIES   ARISING   FEOM   THE   USE    OF   INVALID   DILEMMAS. 

The  nature,  appropriate  sphere,  and  use  of  the  dilemma  have 
been  fully  set  forth  in  the  Analytic.  We  would  simply  allude, 
in  this  connection,  to  certain  quite  common  fallacies  which  arise 
from  the  use  of  invalid  syllogisms  of  this  character. 

One  of  the  most  common  forms  is  this  :  An  individual,  wish- 
ing to  embarrass  an  opponent,  puts  a  question  and  demands  a 
direct  categorical  answer  to  it  in  this  form — yes  or  no.  The 
question  answered  in  this  form,  may  appear,  at  least,  whichever 
answer  is  returned,  to  involve  the  respondent  in  palpable  con- 
tradiction. At  the  same  time,  if  the  question  is  answered  with 
needful  explanations,  this  difficulty  will  wholly  disappear.  The 
questioner  denies  the  right  of  explanation,  and  insists  upon  the 
specific  form  of  answer  referred  to.  Now,  in  such  cases,  a  di- 
lemma with  no  real  horns  is  presented,  while  the  presentation 
of  it  reveals  the  dishonesty  of  the  questioner  and  nothing  else. 
The  question  put  to  our  Saviour,  "  Is  it  lawful  to  give  tribute 
to  Csesar,  or  not  ?  shall  we  give,  or  shall  we  not  give  ?"  is  of 
this  character.  Answered  with  appropriate  explanations,  the 
difficulty  wholly  disappeared. 

Another  form  of  this  fallacy  consists  in  presenting  a  case  as 
admitting  of  but  one  of  two  answers,  when,  in  fact,  other  hy- 
potheses are  equally  supposable.  Thus  the  question  of  the  Sad- 
ducees  to  our  Saviour,  pertaining  to  the  resurrection,  assumed 
that  the  doctrine  of  the  resurrection  is  not  true,  or  individuals 
are,  in  that  state,  "  married  and  given  in  marriage,"  and  that 
those  who  have  been  married  here  must  continue  in  that  rela- 
tion there.  The  case  was  relieved  at  once  of  all  difficulty  by 
the  revelation  of  the  false  assumption  named,  in  respect  to  the 
state  to  which  the  spirit  is  raised  in  the  resurrection. 


252  logic. 

A  dilemma,  to  be  valid,  must  have  these  characteristics : 
1.  The  case  presented  must  have  a  necessary  connection  with 
the  circumstances  to  which  it  is  referred.  2.  It  must  present 
the  only  possible  hypotheses  permitted  by  the  circumstances. 
3.  The  individual  pushed  by  the  presentation  must  be  necessi- 
tated to  adopt  one  or  the  other  of  the  hypotheses  presented 
as  true.  4.  Each  alike  must  be  fatal  to  his  cause.  Of  this 
character  is  the  dilemma  presented  by  Demosthenes,  so  often 
cited.  Any  case  not  possessed  of  all  these  characteristics,  is 
a  dilemma  without  horns,  that  is,  an  argument  which  proves 
nothing  at  all. 

CONCLUSIONS   BASED   UPON   FALSE   ANALOGIES. 

We  have  already  given  the  principles  in  conformity  to 
which  alone  the  argument  from  analogy  has  force.  Conclusions 
based  upon  resemblances  void  of  these  characteristics,  rest 
upon  premises  Avhich  of  course  prove  nothing.  Now  this  is 
one  of  the  most  common  forms  of  fallacy  to  be  met  with — the 
assumption  that  cases  are  analogous  when  they  are  not.  We 
give  the  following  example  and  refutation  of  a  false  analogy, 
from  Bishop  Butler : 

"  There  is  little  presumption  that  death  is  the  destruction  of 
human  creatures.  However  there  is  the  shadow  of  an  analogy, 
which  may  lead  us  to  imagine  it  is— the  supposed  likeness  which 
is  observed  between  the  decay  of  vegetables  and  of  living  crea- 
tures. And  this  likeness  is,  indeed,  sufficient  to  afford  the  poets 
very  apt  allusions  to  the  flowers  of  the  field,  in  their  pictures  of 
the  frailty  of  our  present  life.  But,  in  reason,  the  analogy  is  so 
far  from  holding,  that  there  appears  no  ground  even  for  the 
comparison  as  to  the  present  question,  because  one  of  the  two 
subjects  compared  is  wholly  void  of  that  which  is  the  principal 
and  chief  thing  in  the  other,  the  power  of  perception  and  of  ac- 
tion ;  and  which  is  the  only  thing  we  are  inquiring  about  the 
continuance  of.  So  that  the  destruction  of  a  vegetable  is  an 
event  not  similar  or  analogous  to  the  destruction  of  a  living 
agent." 


DOCTRINE     OF     FALLACIES.  253 

"  This  may  be  resolved,"  says  Mr.  Thomson,  "  into  two  syl- 
logisms : 

I. — Analogy — in  AUA,  Fig.  III. 
The  decay  of  vegetables  is  total  destruction  ; 

The  decay  of  vegetables  =  (for  present  purposes)  the  decay  of  living  crea- 
tures ; 
Therefore,  the  decay  of  living  creatures  is  total  destruction. 

II. — Refutation. 
The  decay  of  animals  is  that  of  living,  acting  creatures  ; 
The  decay  of  vegetables  is  not  that  of  living,  acting  creatures  ; 
Therefore,  the  decay  of  vegetables  is  not  the  same  as  that  of  animals. 

The  conclusion  E  of  the  latter  syllogism,  is  opposed  as  a  contra- 
ry to  the  premise  U  of  the  former." 

The  reader  will  notice,  on  reflecting  upon  the  previous  exam- 
ples and  illustrations,  that  there  are  two  kinds  of  premises 
which  lead  to  no  valid  conclusions  whatever :  those  which,  if 
admitted,  authorize  no  conclusions  of  any  kind,  such  as  two 
negative  or  particular  premises,  and  where  there  is  an  undis- 
tributed middle,  &c. ;  and  those  in  which  one  or  both  of  the 
premises  are  themselves  unduly  assumed.  Both  classes  of 
premises,  though  for  somewhat  different  reasons,  are  equally 
void  of  all  consequence  as  far  as  valid  conclusions  are  con- 
cerned. 


Section  II. — Conclusions  deduced  from  Premises  which 

COME   SHORT   OF   PROVING   SAID   CONCLUSIONS. 

All  are  aware  that  conclusions  are  often  deduced  from  prem- 
ises which  have  some  bearing  upon  said  conclusions,  but  which 
fail  utterly  to  prove  them  in  full.  This  class  of  fallacies  next 
claims  our  attention,  among  which  we  notice  the  following  : 

Drawing  a  universal  conclusion,  where  only  a  particular  is 
allowable. 
One  of  the  most  common  fallacies  of  this  class  is  the  assump- 
tion of  a  universal  conclusion,  when  only  a  particular  one  is 


allowed  by  the  premises.  Suppose  that  it  becomes  known,  or 
has  been  proven,  that  certain  individuals  of  a  certain  class  have 
some  particular  characteristic.  Almost  nothing  is  more  com- 
mon than  to  draw  from  hence  the  conclusion,  that  the  same 
characteristic  pertains  to  the  entire  class.  Individuals  are  most 
likely  to  be  deceived  by  such  a  course  of  reasoning  when  the 
cases  cited  are  quite  numerous.  What  is  shown  to  be  general- 
ly true,  is  very  readily  assumed  to  be  universally  so.  In  such 
circumstances  we  should  be,  in  a  very  special  manner,  on  our 
guard. 

Proving  a  part  of  a  conclusion  and  then  assuming  the  whole 
as  established. 

When  the  proposition  to  be  proved  is  made  up  of  several 
parts,  and  some  of  these  have  been  proved  or  disproved,  a  skil- 
ful sophist,  by  greatly  enlarging  upon  these,  will  assume,  and 
often  induce  others  to  do  the  same,  that  all  the  parts  have  been 
proved  or  disproved,  when  the  main  issue  has  not  been  touched 
at  all. 

"  This,"  says  Dr.  Whately,  "  is  the  great  art  of  the  answerer 
of  a  book  ;  suppose  the  main  positions  in  any  work  to  be  irre- 
fragable, it  will  be  strange  if  some  illustration  of  them,  or  some 
subordinate  part,  in  short,  will  not  admit  of  a  plausible  objec- 
tion ;  the  opponent  then  joins  issue  on  one  of  these  incidental 
questions,  and  comes  forward  with  '  a  reply'  to  such  and  such  a 
work. 

"  Hence  the  danger  of  ever  advancing  more  than  can  be  well 
maintained,  since  the  refutation  of  that  will  often  quash  the 
whole ;  a  guilty  person  may  often  escape  by  having  too  much 
laid  to  his  charge ;  so  he  may  also  by  having  too  much  evi- 
dence against  him,  i.  e.  some  that  is  not  in  itself  satisfactory ; 
thus,  a  prisoner  may  sometimes  obtain  acquittal  by  showing 
that  one  of  the  witnesses  against  him  is  an  informer  and  spy ; 
though  perhaps  if  that  part  of  the  evidence  had  been  omitted, 
the  rest  would  have  been  sufficient  for  conviction.'' 


l  yv 


DOCTEIKE     OF     FALLACIES.  255 

Fallacy  of  Objections. 

■  Fallacy  of  objections,  which  next  claims  our  attention,  con- 
sists, in  the  language  of  Dr.  Whately,  in  "  showing  that  there 
are  objections  against  some  plan,  theory,  or  system,  and  thence 
inferring  that  it  should  be  rejected ;  when  that  which  ought  to 
have  been  proved  is,  that  there  are  more  or  stronger  objections 
against  the  receiving  than  the  rejecting  it.  This  is  the  main 
and  almost  universal  fallacy  of  infidels,  and  is  that  of  which 
men  should  be  first  and  principally  warned.  This  is  also  the 
stronghold  of  bigoted  anti-innovators,  who  oppose  all  reforms 
and  alterations  indiscriminately ;  for  there  never  was,  nor  will 
be,  any  plan  executed  or  proposed  against  which  strong  and 
even  unanswerable  objections  may  not  be  urged ;  so  that,  un- 
less the  opposite  objections  be  set  in  the  balance  on  the  other 
side,  we  can  never  advance  a  step.  '  There  are  objections,' 
said  Dr.  Johnson,  '  against  a  plenum,  and  objections  against  a 
vacuum  /  but  one  of  them  must  be  true.' 

"  The  very  same  fallacy,  indeed,  is  employed  on  the  other 
side,  by  those  who  are  for  overthrowing  whatever  is  established 
as  soon  as  they  can  prove  an  objection  against  it,  without  con- 
sidering whether  more  and  weightier  objections  may  not  lie 
against  their  own  schemes  ;  but  their  opponents  have  this  de- 
cided advantage  over  thejn,  that  they  can  urge  with  great  plau- 
sibility, '  we  do  not  call  upon  you  to  reject  at  once  whatever  is 
objected  to,  but  merely  to  suspend  your  judgment,  and  not 
come  to  a  decision  as  long  as  there  are  reasons  on  both  sides ;' 
now,  since  there  always  will  be  reasons  on  both  sides,  this  non- 
decision  is  practically  the  very  same  thing  as  a  decision  in  fa- 
vor of  the  existing  state  of  things ;  the  delay  of  trial  becomes 
equivalent  to  an  acquittals 


The  object  sought  to  be  established  in  processes  of  reasoning 
is,  in  some  instances,  not  the  positive  but  probable.  When  the 
latter  is  the  character  of  the  conclusion  sought,  a  fallacy  of  this 


256  LOGIC. 

kind  often  appears,  to  wit :  when  one  degree  and  form  of  proba- 
bilities is  proven,  another  is  assumed  as  established.  To  under- 
stand this  subject  we  would  remark,  that  probabilities  are  of 
two  kinds  ;  one  is,  where  a  number  of  propositions  sustain  such 
relations  to  a  given  one,  that  if  any  of  them  is  true,  the  one 
referred  to  either  is  or  is  not  probably  true,  while  each  of  these 
propositions  has  a  certain  independent  degree  of  probability  of 
being  true,  as  one  to  two,  for  example.  Suppose  that  the  num- 
ber of  such  propositions  is  six  ;  then,  supposing  the  connection 
above-named  to  be  certain,  the  probability  of  the  common  con- 
sequent of  said  proposition  being  true  is  as  six  to  one.  If  the 
connection  is  only  a  probable  one,  say  as  one  to  two,  then  the 
probability  under  consideration  is  as  three  to  one.  Probabili- 
ties of  this  character  may  be  so  multiplied  as  to  exclude  all  rea- 
sonable doubt. 

The  second  form  of  probability  arises,  when  each  probability 
depends  upon  another,  and  so  on  to  the  last,  somewhat  in  the 
form  of  a  sorites  ;  as,  A  is  probably  B,  B  is  probably  C,  &c. ; 
therefore,  A  is  probably  C.  Let  us  suppose  that  the  ratio  of 
probability  in  each  is  as  above,  as  one  to  two.  In  this  case  the 
probability  that  A  is  C  is  only  as  one  to  sixteen.  In  this  case, 
too,  when  the  series  of  probabilities  is  very  long,  all  reasonable 
expectation  that  the  proposition  referred  to  can  be  true  is  ex- 
cluded. 

Now  the  fallacy  to  which  we  refer  consists  in  confounding 
these  two  kinds  of  probability,  and  assuming  one  as  proven, 
when  the  other  only  has  been.  Suppose,  for  example,  there  is 
an  attempt  to  prove  a  proposition  sustained  by  probabilities  of 
the  first  class.  An  opponent,  in  replying,  may  dilate  on  the 
uncertainty  of  probable  evidence,  drawing  all  his  examples 
from  the  second  class,  and  yet  so  presenting  them,  that  the 
characteristics  of  the  two  shall  be  confounded  in  the  hearer's  or 
reader's  mind,  and  thus  the  force  of  the  evidence  destroyed. 
Suppose,  on  the  other  hand,  an  individual  desires  to  prove  a 
proposition  sustained  exclusively  by  probabilities  of  the  second 
class.  He  will,  of  course,  dilate  upon  the  safety  of  resting  upon 
probable  evidence,  showing  how  all  the  transactions  of  life  have 


DOCTRINE     OP     FALLACIES.  257 

no  other  foundation,  taking  his  examples  and  illustrations  from 
the  first  class,  keeping  out  of  view,  as  far  as  possible,  the  nature 
of  the  probabilities  with  which  he  has  to  do.  Nothing  is  more 
important  in  judging  of  such  arguments,  than  to  keep  distinct- 
ly in  mind  the  diverse  and  opposite  character  of  these  two  kinds 
of  probability,  and  to  mark  clearly  the  special  kind  which  en- 
ters into  the  process  which  is  the  subject  of  investigation. 


Section  III. — Conclusions  deduced  from  Premises  which 

PROVE    NOT   THOSE   REALTY   SOUGHT  TO   BE  PROVED,   BUT   CER- 
TAIN   OTHER   AND   IRRELEVANT    ONES. 

The  only  remaining  topic  of  remark  is  that  class  of  fallacies 
in  which  false  inferences  are  deduced  from  premises  which 
prove,  not  the  conclusion  really  sought,  but  something  else 
which  is  irrelevant.  Under  this  head  we  have  two  classes  of 
irrelevant  conclusions,  those  in  which  the  conclusion  sought  is 
inferred  from  premises  which  prove,  not  said  conclusions,  but 
something  else ;  and  those  in  which  something  assumed  as  the 
real  conclusion  sought,  but  which  is  not,  is  proved  or  attempted 
to  be. 

Ignoratio  elenchi,  or  Irrelevant  Conclusion. 

Fallacies  of  the  second  class  named  constitute  especially  what 
is  commonly  called  the  ignoratio  elenchi,  or  irrelevant  conclu- 
sion, a  fallacy  which  consists  in  a  proof,  or  an  attempted  one, 
of  a  certain  proposition  assumed  to  be  the  real  one,  when  it  is 
not.  The  example  commonly  adduced  in  illustration  of  this 
kind  of  fallacy  is  given  by  Dr.  Whately  in  the  following  lan- 
guage :  "  A  good  instance  of  the*  employment  and  exposure  of 
this  fallacy  occurs  in  Thucydides,  in  the  speeches  of  Cleon  and 
Diodotus  concerning  the  Mitylenoeans ;  the  former  (over  and 
above  his  appeal  to  the  angry  passions  of  his  audience)  urges 
the  justice  of  putting  the  revolters  to  death  ;  which,  as  the  lat- 
ter remarked,  was  nothing  to  the  purpose,  since  the  Athenians 


«w 


G  aM^ 


258  logic. 

were  not  sitting  in  judgment,  but  in  deliberation,  of  which  the 
proper  end  is  expediency." 

When  we  were  studying  theology,  a  very  distinguished  and 
celebrated  professor  of  that  science  delivered  to  us  a  course  of 
lectures — first,  on  the  doctrine  of  necessity  and  the  Divine  sov- 
ereignty ;  and  then,  on  the  question  of  man's  freedom  and  ac- 
countability for  his  actions  and  mental  states.  These  two  ques- 
tions were"  discussed  separately,  and  professedly  settled  by  en- 
tirely independent  trains  of  argumentation.  Finally,  the  ques- 
tion, How  can  these  doctrines  be  reconciled  ?  was  propounded 
for  discussion,  and  was  actually  disposed  of  thus :  "  We  have 
proved,"  said  the  learned  professor,  "  that  these  two  great  doc- 
trines are  each  true,  that  is,  they  do  both  exist,  as  a  matter  of 
fact ;  that  is,  they  exist  together  ;  that  is,  they  coexist ;  that  is, 
they  cosist ;  that  is,  they  consist  or  are  consistent." 

This  was  overwhelmingly  convincing  to  a  majority  of  the  au- 
dience. Who  does  not  perceive,  however,  1.  That  in  this  de- 
partment of  investigation,  the  question  of  consistency  in  the 
sense  of  real  compatibility,  and  not  consistency,  in  the  sense 
of  coexistence,  was  the  question  to  be  settled ;  and,  2.  That, 
as  two  incompatible  propositions  can,  by  no  force  of  argumen- 
tation, be  both  proved  to  be  true,  any  more  than  we  can  prove 
that  the  same  thing  can  at  the  same  time  exist  and  not  exist, 
when  the  question  of  compatibility  is  raised,  all  arguments  to 
prove  both  true  must  be  held  as  invalid,  till  this  one  is  settled. 
Here,  then,  was  a  very  striking  example  of  the  ignoratio  elenchi. 

As  this  is  a  very  important  department  of  inquiry,  we  will 
venture  to  give  another  example  from  a  very  important  and 
valuable  work  oh  "Systematic  Theology,"  a  work  originally 
put  forth  in  this  country,  and  then,  with  many  corrections  and 
enlargements,  republished  in  England,  by  my  former  most 
highly  esteemed  and  beloved  associate,  President  C.  G.  Finney. 
In  each  edition  of  this  work,  the  question  as  to  the  foundation 
of  obligation  is  discussed  at  great  length.  In  the  first,  frequent 
quotations  are  made  from  lectures  of  mine  which  were  printed 
for  the  accommodation  of  students,  but  not  published — quota- 
tions, without  giving  names  or  references.     As  the  source,  how- 


DOCTRINE     OF     FALLACIES.  259 

ever,  was  known,  my  views  were  being  presented  in  a  form  in 
which  I  clearly  saw  they  would  be,  and  were  being,  misunder- 
stood. This  occasioned,  when  my  work  on  moral  philosophy 
was  published,  a  full  examination  of  the  question  in  respect  to 
which  President  Finney's  and  my  own  investigations  had  led 
us  to  adopt  different  and  opposite  views  upon  the  subject.  To 
accomplish  this  object  I  first  gave  a  distinct  statement  of  the 
.  two  theories,  his  and  my  own,  with  their  points  01  agreement 
and  disagreement.  I  will  give  the  statement  of  the  two  theo- 
ries as  found  in  this  chapter :  I  do  it  for  two  reasons — the  turn- 
ing of  thought  to  an  important  question  in  morals,  and  as  an 
example  of  the  manner  in  which,  when  conflicting  views  are  to 
be  discussed,  the  questions  at  issue  should  be  presented. 

"  President  Finney'' s  Statement. 

To  attain  the  object  in  view,  the  first  thing  to  be  done  is  to 
ascertain  clearly  what  this  theory  is,  as  distinguished  from  that 
maintained  in  this  treatise.  Professor  Finney  fully  agrees  with 
myself  in  rejecting  the  doctrine  of  utility.  '  The  teachings  of 
a  consistent  utilitarian,'  he  says,  'must  of  necessity  abound 
'  with  pernicious  error.'  Again  :  '  Consistent  utilitarianism  in- 
culcates fundamentally  false  ideas  of  the  nature  of  virtue.'  Of 
course,  he  will  agree  with  me  in  the  statement  made  in  the  last 
chapter,  that  any  theory  (his  own  not  excepted)  that,  in  its 
logical  consequences,  necessarily  lands  us  hi  this  doctrine,  must 
be  false.     What  then  is  this  theory  ? 

1.  He  maintains  that  the  only  ultimate  reason  in  view  of 
which  obligation  is  ever  affirmed,  is  happiness  as  a  good  in  itself. 
*  It  is,  then,  the  intrinsic  and  infinite  value,'  he  says,  '  of  the 
highest  good  of  God  and  of  the  universe,  that  constitutes  the 
true  foundation  of  moral  obligation.' 

2.  He  maintains  that  obligation  in  no  form  or  degree  is  ever 
affirmed  in  view  of  what  is  perceived  to  be  intrinsic  in  moral 
character,  holiness  or  sin,  virtue  or  vice,  merit  or  demerit. 
None  of  these  contain  any  ultimate  reason  for  any  acts  of  will 
whatever.     '  The  highest  well-being  of  God  and  of  the  universe 


260  LOGIC. 

of  sentient  creatures  is  the  end  on  which  preference,  choice,  in- 
tention, ought  to  terminate.' 

3.  Holiness  or  sin,  moral  character,  &c,  are  esteemed  by  the 
mind  for  no  other  reason  than  as  a  condition  or  a  means  of 
happiness. 

'  Obedience  must  be  a  means  or  condition,  and  that  which 
law  and  obedience  are  intended  to  secure  is,  and  must  be, 
the  ultimate  end  of  obedience.  The  law  or  the  lawgiver  aims 
to  promote  the  highest  good  or  blessedness  of  the  universe. 
This  must  be  the  end  of  moral  law  and  moral  government. 
Law  and  obedience  must  be  the  means  or  conditions  of  this 
end.    It  is  absurd  to  deny  this.' 

Again,  speaking  of  virtue,  moral  worth,  &c,  he  says : 

1  Were  it  not  for  the  fact,  that  it  meets  a  demand  of  the  in- 
telligence and  thus  produces  satisfaction,  it  could  not  so  much 
as  be  thought  of  as  a  good  in  itself,  any  more  than  any  thing 
else  that  is  a  pure  conception  of  the  reason,  such,  for  instance, 
as  a  mathematical  line.'     Further  on,  he  adds  : 

'  The  willing  and  the  worthiness  of  willing  are  valuable 
only  as  the  end  willed  is  valuable.  Were  it  not  that  the  end  is 
intrinsically  valuable,  the  willing  would  not  be  so  much  as 
relatively  valuable.    It  would  have  no  value  whatever.' 

4.  The  intelligence  does  not  require  ultimate  intentions,  in 
other  words,  does  not  affirm  obligation  in  respect  to  them,  as  a 
condition  or  a  means  of  happiness  is  a  good  in  itself.  This  sen- 
timent is  often  repeated  in  the  work  before  us.  A  single  quota- 
tion, however,  is  all  that  is  necessary  to  show  that  I  have  right- 
ly expounded  the  view  therein  set  forth  on  this  point : 

'  Ultimate  intention  is  right  or  wrong  in  itself,  and  no  ques- 
tions of  utility,  expediency,  or  tendency  have  any  thing  to  do 
with  the  obligation  to  put  forth  ultimate  intention,  there  being 
only  one  reason  for  this,  namely,  the  intrinsic  value  of  the  end 
to  be  intended.  It  is  true  that  whatever  is  expedient  is  right, 
not  for  that  reason,  but  only  upon  that  condition.  The  inquiry, 
then,  Is  it  expedient  ?  in  respect  to  outward  action  is  always 
proper ;  for  upon  this  condition  does  obligation  to  outward  ac- 
tion turn.     But  in  respect  to  ultimate  intention  or  the  choice  of 


DOCTRINE  OF  FALLACIES.  261 

an  ultimate  end,  an  inquiry  into  the  expediency  of  this  choice 
or  intention  is  never  proper,  the  obligation  being  founded  alone 
upon  the  perceived  and  intrinsic  value  of  the  end,  and  the  obli- 
gation being  without  any  condition  whatever,  except  the  pos- 
session of  the  powers  of  moral  agency  with  the  perception  of 
the  end  upon  which  intention  ought  to  terminate,  namely,  the 
good  of  universal  being.' 

5.  While  obligation  to  put  forth  ultimate  intentions  is  in  no 
sense  conditioned  upon  their  perceived  tendency  to  promote 
happiness,  the  necessary  condition  of  obligation  to  put  forth 
executive  volitions  and  outward  actions  is  their  perceived  ten- 
dency to  promote  happiness.  '  I  said,  in  a  former  lecture,  that 
the  obligation  to  put  forth  volitions  or  outward  actions  to  se- 
cure an  end  must  be  conditioned  upon  the  perceived  tendency 
of  such  volitions  and  actions  to  secure  that  end  ;  but  while  this 
tendency  is  the  condition  of  the  obligation  to  executive  volition 
or  outward  action,  the  obligation  is  founded  upon  the  intrinsic 
value  of  the  end,  to  secure  which  such  volitions  tend.' 

The  Opposite  Theory  stated. 

Such  is  the  doctrine  set  forth  in  the  treatise  on  Systematic 
Theology.  Let  us  now  attend  to  a  statement  of  the  opposite 
theory : 

1.  The  advocates  of  this  theory  agree  with  Professor  Finney 
in  the  doctrine,  that  the  good  of  being  is  an  ultimate  reason  for 
ultimate  intentions  of  a  certain  class,  to  wit,  all  intentions  in- 
cluded in  the  words — willing  the  good  of  being. 

2.  On  the  other  hand,  they  affirm,  that  there  are  other  ob- 
jects, such  as  virtue  and  sin,  moral  character,  moral  desert,  «fcc., 
which  contain  ultimate  reasons  for  certain  acts  of  will  or  ulti- 
mate intentions,  besides  happiness  as  a  good  in  itself.  Here, 
and  here  only,  is  there  a  difference  of  opinion.  The  doctrine 
maintained  by  this  class  of  philosophers  may  be  thus  stated : 
Whenever  an  object  is  present  to  the  mind,  which,  on  account 
of  what  is  intrinsic  in  the  object  itself,  necessitates  the  will  to 
act,  two  or  more  distinct  and  opposite  acts  are  always  possible 


262  logic. 

relatively  to  such  object.  The  intelligence  can  never  be  indif- 
ferent in  respect  to  the  acts  or  intentions  put  forth  under  such 
circumstances.  In  its  judgment  that  act,  and  that  act  only,  can 
be  right  which  corresponds  with  the  apprehended  intrinsic  char- 
acter of  the  object.  All  other  acts  must  be  wrong.  The  sphere 
of  moral  obligation  must  be  as  extensive  as  the  objects  the  ap- 
prehension of  which  intrinsically  necessitate  acts  of  will  of  some 
kind,  and  relatively  to  which  distinct  and  opposite  acts  are  pos- 
sible. According  to  Professor  Finney,  there  is  but  one  object 
in  existence  the  apprehension  of  which  intrinsically  necessitates 
acts  of  will,  to  wit,  the  good  of  being.  According  to  this  class 
of  philosophers,  there  are  other  objects  aside  from  this,  the  ap- 
prehension of  which  also  necessitates  acts  of  will,  and  relatively 
to  which,  therefore,  obligation  does  and  must  pertain.  We  are 
now  prepared  for  a  distinct  statement  of  the  arguments  which 
he  against  the  theory  of  Professor  Finney,  and  in  favor  of  the 
opposite  theory," 

I  then,  in  ten  distinct  arguments  and  nine  general  state- 
ments, argue  the  single  issue  here  presented.  In  the  English 
edition  of  his  great  work,  President  Finney  gives  a  professed 
reply  to  this  presentation.  "What  is  that  reply  ?  No  correc- 
tions are  offered  of  my  statements  of  the  two  theories,  and  the 
issue  presented.  All  here  is  thus  admitted  to  be  correct.  I  am 
equally  safe  in  saying,  that  not  one  of  my  arguments  has  been 
met,  and  to  but  very  few  of  them  is  there  even  a  remote  allu- 
sion. On  the  other  hand,  I  am  held  before  the  people  of  Eng- 
land as  asserting,  in  different  parts  of  my  works,  some  half  a 
dozen  or  more  distinct  and  opposite  theories  pertaining  to  the 
foundation  of  obligation.  In  no  instance  is  my  language  cited. 
On  the  other  hand,  a  bear  reference  is  made  to  the  work.  Had 
he  given  quotations  in  full,  the  people  of  England  would  have 
seen,  not  that  I  have  asserted  these  contradictory  theories: — for 
I  have  done  no  such  thing — but  that  my  deeply-respected  asso- 
ciate has  most  honestly,  without  a  shadow  of  a  doubt,  himself 
misunderstood  me.*     But  what  has  this  to  do  with  the  ques- 

*  I  will  give  an  example  or  two  in  illustration.  On  pages  85-86  I  give  two  formulas  for 
the  announcement  of  the  true  doctrine  of  the  foundation  of  obligation,  the  first  as  incom- 


r 


DOCTRINE     OF     FALLACIES.  263 

tion  at  issue  ?  Absolutely  nothing.  If  I  have  asserted  such 
theories  in  another  part  of  the  hook,  I  have  done  no  such  thing 
in  this  one  department  of  it.  Here  but  two  theories  stand  re- 
vealed, and  but  a  single  issue  is  presented,  and  every  thing 
bears  directly  and  exclusively  upon  that  issue.  What  an  exam- 
ple of  the  real  ignoratio  elenchi  is  it,  to  divert  attention  from 
this  single  issue  to  another  and  different  one,  to  wit,  whether 
in  other  parts  of  my  work  self-consistency  is  maintained.  Yet 
this  is  a  form  of  fallacy  most  common  in  community. 

Suppressing  the  Conclusion. 

One  of  the  most  effectual  modes  of  accomplishing  this  result 
is  suppressing  the  real  question,  and  with  logical  precision  argu- 
ing some  analogous  or  similar,  yet  in  reality  distinct  question, 
as  if  it  was  the  real  one. 

Suppose  that  the  real  question  in  a  given  case  is,  whether  an 
individual  on  a  given  occasion  committed  some  specific  crime. 
His  accuser,  wholly  unable  to  prove  that  single  point,  makes  a 
violent  assault  upon  his  general  character,  and  dilates  with  in- 
tense earnestness  upon  this,  omitting  to  inform  his  auditory, 
that  not  general  character,  but  a  specific  act  at  a  specific  time, 
is  the  exclusive  subject  of  inquiry.  On  the  other  hand,  suppose 
that  not  specific  acts,  but  general  character,  is  the  subject  of  dis- 
cussion.    Suppose  that  here,  if  the  real  issue  is  exclusively  pre- 

plete  and  imperfect  and  so  far  wrong;  and  the  second,  as  announcing  the  doctrine  with 
"  philosophic  precision."  All  this  is  fully  and  distinctly  stated.  After  saying  this,  I  state 
that  the  first  formula  is  not,  and  the  second  is,  the  true  one.  Yet,  in  the  "  Systematic  The- 
ology," these  two  formulas  are  given,  and  I  am  represented  as  having  announced  each  alike 
as  unqualifiedly  correct,  and  thus  palpably  contradicted  myself. 

Again,  on  page  36,  I  am  represented  as  teaching  the  doctrine  that  "the  idea  of  right  is  the 
foundation  of  obligation."  In  that  place  I  am  speaking  of  the  relative  order  of  the  ideas 
of  right  and  wrong,  of  obligation,  moral  desert,  and  retribution.  I  then,  in  accordance  with 
the  teachings  of  all  philosophers  that  I  am  acquainted  with,  speak  of  these  ideas  as  resting 
immediately  one  upon  the  other,  in  the  order  above  stated.  This  is  the  exclusive  sense  in 
which  I  am  there  speaking  upon  this  subject.  When,  in  another  place,  I  come  to  discuss 
the  true  and  proper  question  of  the  foundation  of  obligation,  I  there  state  it  in  form  to  be 
synonymous  with  the  question,  What  is  the  foundation  of  the  idea  of  right?  There  I  say 
that  that  "  which  renders  in  the  judgment  of  the  intelligence  one  action  necessarily  right, 
and  all  others  (of  an  opposite  nature)  wrong,"  is  "  the  foundation  of  obligation."  In  thia 
form  exclusively  have  I  discussed  the  subject  in  my  Intellectual  and  Moral  Philosophy 
both.    The  examples  speak  for  themselves— and  here  I  leave  the  subject 


264  logic. 

sented,  the  virtue  of  the  accused  will  appear  unblemished.  An 
opponent  may  attempt  to  gain  his  end  by  pushing  forward 
some  specific  acts  of  a  questionable  character,  and  by  enlarging 
upon  them  aim  to  secure  a  verdict  against  the  character  of  the 
accused.  Sometimes  the  person  accused  gives  strength  to  this 
form  of  attack,  by  attempting  to  defend  himself  on  every  point, 
as  if  this,  and  not  the  question  of  general  character,  is  the  ex- 
clusive issue.  In  all  such  cases  general  character  is  best  de- 
fended by  admitting  and  confessing  all  individual  aberrations. 
The  very  confession  is  a  vindication  of  general  character. 

ARGUMENTUM   AD   HOMIKEM. 

There  are  two  forms  in  which  what  is  called  the  argumen- 
tum ad  hominem  may  be  properly  employed.  The  first  we 
have  already  considered,  and  consists  in  showing  that  the  argu- 
ment of  the  opponent  proves  too  much,  and  therefore  is  false. 
The  second,  which  we  are  now  to  consider  as  properly  belong- 
ing to  this  division  of  our  subject,  consists  in  showing  that  from 
his  own  acknowledged  principles,  an  opponent  is  bound  in  con- 
sistency to  admit  the  conclusion  urged  upon  him.  This  is  a  le- 
gitimate form  of  argument  when  properly  used.  The  fallacy 
connected  with  it  consists,  not  in  showing  that  consistency  re- 
quires the  individual  referred  to  to  admit  said  conclusion,  but 
in  assuming  that  conclusion  as  really  thereby  proved  as  true  in 
itself.  This  fallacy  has  been  so  well  elucidated  by  Dr.  Whate- 
ly,  that  we  will  venture  another  citation  from  him,  and  with  it 
close  our  remarks  upon  this  subject : 

"  There  are  certain  kinds  of  argument  recounted  and  named 
by  logical  writers,  which  we  should  by  no  means  universally 
call  fallacies  ;  but  which  when  unfairly  used,  and  so  far  as  they 
are  fallacious,  may  very  well  be  referred  to  the  present  head  ; 
such  as  the  '  argumentum  ad  hominemf  or  personal  argument, 
' argumentum  ad  verecundiamf  ''argumentum  ad  populumf 
&c,  all  of  them  regarded  as  contradistinguished  from  ''argu- 
mentum ad  rem,'1  or,  according  to  others  (meaning  probably 
the  very  same  thing),  '  ad  judicium.''     These  have  all  been  de- 


DOCTRINE     OF     FALLACIES.  265 

scribed  in  the  lax  and  popular  language  before  alluded  to,  but 
not  scientifically :  '  the  "  argumentum  ad  hominem," '  they  say, 
'is  addressed  to  the  peculiar  circumstances,  character,  avowed 
opinions,  or  past  conduct  of  the  individual,  and  therefore  has  a 
reference  to  him  only,  and  does  not  bear  directly  and  absolute- 
ly on  the  real  question,  as  the  "  argumentum  ad  rem''''  does ;'  in 
like  manner,  the  '  argumentum  ad  verecundiam)  is  described  as 
an  appeal  to  our  reverence  for  some  respected  authority,  some 
venerable  institution,  &c,  and  the  '  argumentum  ad  populumj 
as  an  appeal  to  the  prejudices,  passions,  &c,  of  the  multitude  ; 
and  so  of  the  rest.  Along  with  these  is  usually  enumerated 
'  argumentum  ad  ignorantiam^  which  is  here  omitted,  as  being 
evidently  nothing  more  than  the  employment  of  some  kind  of 
fallacy,  in  the  widest  sense  of  that  word,  towards  such  as  are 
likely  to  be  deceived  by  it.  It  appears  then  (to  speak  rather 
more  technically)  that  in  the> '  argumentum  ad  hominem?  the 
conclusion  which  actually  is  established,  is  not  the  absolute  and 
general  one  in  question,  but  relative  and  particular ;  viz.,  not 
that  '  such  and  such  is  the  fact,'  but  that  '  this  man  is  bound  to 
admit  it,  in  conformity  to  his  principles  of  reasoning,  or  in  con- 
sistency with  his  own  conduct,  situation,'  &c  *  Such  a  conclu- 
sion it  is  often  both  allowable  and  necessary  to  establish  in 
order  to  silence  those  who  will  not  yield  to  fair  general  argu- 
ment ;  or  to  convince  those  whose  weakness  and  prejudices 
would  not  allow  them  to  assign  to  it  its  due  weight ;  it  is  thus 

*  "The  ' argumentum  ad  hominenC  will  often  have  the  effect  of  shifting  the  burden  of 
proof,  not  unjustly,  to  the  .adversary.  A  common  instance  is  the  defence,  certainly  the 
readiest  and  most  concise,  frequently  urged  by  the  Sporstman,  when  accused  of  barbarity 
in  sacrificing  unoffending  hares  or  trout  to  his  amusement:  he  replies,  as  he  may  safely  do, 
to  most  of  his  assailants,  '  why  do  you  feed  on  the  flesh  of  animals  ?'  and  that  this  answer 
presses  hard,  is  manifested  by  its  being  usually  opposed  by  a  palpable  felsehood ;  viz.,  lhat 
the  animals  which  are  killed  for  food  are  sacrificed  to  our  necessities;  though  not  only 
men  can,  but  a  large  proportion  (probably  a  great  majority)  of  the  human  race  actually  do, 
subsist  in  health  and  vigor  without  flesh-diet;  and  the  earth  would  support  a  much  greater 
human  population  were  such  a  practice  universal.  When  shamed  out  of  this  argument,  they 
sometimes  urge  that  the  brute  creation  would  overrun  the  earth,  if  we  did  not  kill  them  for 
food;  an  argument,  which,  if  it  were  valid  at  all,  would  not  justify  their  feeding  on  fish  ; 
though,  if  fairly  followed  up,  it  would  justify  Swift's  proposal  for  keeping  down  the  exces- 
sive population  of  Ireland.  The  true  reason,  viz.,  that  they  eat  flesh  for  the  gratification  of 
the  palate,  and  have  a  taste  for  the  pleasures  of  the  table,  though  not  for  the  sports  of  the 
field,  is  one  which  they  do  not  like  to  assign." 
12 


266  LOGIC. 

that  our  Lord  on  many  occasions  silences  the  cavils  of  the  Jews ; 
as  in  the  vindication  of  healing  on  the  Sabbath,  which  is  paral- 
leled by  the  authorized  practice  of  drawing  out  a  beast  that  has 
fallen  into  a  pit.  All  this,  as  we  have  said,  is  perfectly  fair,  pro- 
vided it  be  done  plainly,  and  avowedly  ;  but  if  you  attempt  to 
substitute  this  partial  and  relative  conclusion  for  a  more  general 
one — if  you  triumph  as  having  established  your  proposition  ab- 
solutely and  universally,  from  having  established  it,  in  reality, 
only  as  far  as  it  relates  to  your  opponent,  then  you  are  guilty 
of  a  fallacy  of  the  kind  which  we  are  now  treating  of;  your 
conclusion  is  not  in  reality  that  which  was,  by  your  own  ac- 
count, proposed  to  be  proved  ;  the  fallaciousness  depends  upon 
the  deceit  or  attempt  to  deceive.  The  same  observations  will 
apply  to  '  argumentum,  ad  verecicndiam,"1  and  the  rest. 

"  It  is  very  common  to  employ  an  ambiguous  term  for  the 
purpose  of  introducing  the  fallacy  of  irrelevant  conclusion  ;  i.  e. 
when  you  cannot  prove  your  proposition  in  the  sense  in  which 
it  was  maintained,  to  prove  it  in  some  other  sense  ;  e.  g.  those 
who  contend  against  the  efficacy  of  faith,  usually  employ  that 
word  in  their  arguments  in  the  sense  of  mere  belief,  unaccom- 
panied with  any  moral  or  practical  result,  but  considered  as  a 
mere  intellectual  process ;  and  when  they  have  thus  proved 
their  conclusion,  they  oppose  it  to  one  in  which  the  word  is 
used  in  a  widely  different  sense."* 

*  "  When  the  occasion  or  object  in  question  is  not  such  as  calls  for,  or  as  is  likely  to  excite 
in  those  particular  readers  or  hearers,  the  emotions  required,  it  is  a  common  rhetorical  arti- 
fice to  turn  their  attention  to  some  object  which  will  call  forth  these  feelings;  and  when' 
they  are  too  much  excited  to  be  capable  of  judging  calmly,  it  -will  not  be  difficult  to  turn 
their  passions,  once  roused,  in  the  direction  required,  and  to  make  them  view  the  case  be- 
fore them  in  a  very  different  light.  When  the  metal  is  heated,  it  may  easily  bo  moulded 
into  the  desired  form.  Thus  vehement  indignation  against  some  crime,  may  be  directed 
against  a  person  who  has  not  been  proved  guilty  of  it;  and  vague  declamations  against  cor- 
ruption, oppression,  &c,  or  against  the  mischiefs  of  anarchy ;  with  high-flown  panegyrics 
•>n  liberty,  .rights  of  man,  &c,  or  on  social  order,  justice,  the  constitution,  law,  religion,  &c, 
will  gradually  lead  the  hearers  to  take  for  granted  without  proof,  that  the  measure  proposed 
will  lead  to  these  evils  or  these  advantages ;  and  it  will  in  consequence  become  the  object 
of  groundless  abhorrence  or  admiration.  For  the  very  utterance  of  such  words  as  have  a 
multitude  of  what  may  be  called  stimulating  ideas  associated  with  them,  will  operate  like 
a  charm  on  the  minds,  especially  of  the  ignorant  and  unthinking,  and  raise  such  a  tumult  of 
feeling,  as  will  effectually  blind  their  judgment:  so  that  a  string  of  vague  abuse  or  panegyrio 
will  often  have  the  effect  of  a  train  of  sound  argument."— liheioric,  Part  II.  Chap,  ii 


erate  like 
tumult  ol 
panegyrio 
),  ii.  §  6. 


PART  III. 

THE    DOCTKINE    OF    METHOD. 


TERMS   DEFINED. 

All  thinking  is  according  to  rules  of  some  kind.  Thought, 
too,  is  always,  both  in  writing  and  speaking,  developed  ac- 
cording to  rules.  There  are  perfect  and  imperfect  forms  of 
thought,  and  it  is  equally  true  that  there  are  perfect  and  im- 
perfect methods  or  forms  of  developing  thought.  The  object 
of  the  doctrine  of  method  is  to  develop  those  rules  and  laws  of 
thought,  in  conformity  to  which  the  idea  of  science  in  all  logi- 
cal forms  of  thinking,  may  he  most  perfectly  realized.  In  the 
former  departments  of  the  present  treatise,  we  have  aimed  to 
develop  those  laws  of  thought  to  which  all  valid  logical  think- 
ing must  conform.  Our  present  object  is  to  develop  those  laws 
of  thought  by  which  logical  thinking  may  assume  its  most  per- 
fect forms. 

MEANS  BY  WHICH  THE  LOGICAL   PERFECTION   OF  THOUGHT  MAT 
BE   SECURED. 

The  doctrine  of  method  must  reveal  the  means  or  rules  by 
which  the  logical  perfection  of  thought  may  be  secured.  The 
essential  characteristics  of  such  forms  of  thinking  are  distinct- 
ness, systematic  order,  and  completeness,  so  that  the  mind  at- 
tains to  full  and  distinct  apprehensions  of  the  whole  of  the  sub- 
ject treated  of.  The  distinct  aim  of  the  doctrine  of  method  is 
to  point  out  the  means  by  which  these  elements  of  perfection 
in  logical  thinking  may  be  induced. 


CONDITIONS    ON   WHICH   THESE   ENDS   MAT   BE   SECURED. 

The  conditions  on  which  the  elements  of  perfection  above- 
named  may  he  induced  are  the  following,  to  wit :  proper  defi- 
nition and  exposition  of  the  whole,  and  of  the  principles  and 
parts,  of  the  subject  treated  of;  a  proper  logical  division  of  said 
subject ;  and  a  proper  order  of  presentation  of  the  parts  refer- 
red to.  We  propose  to  elucidate  the  subject  before  us  in  the 
order  named,  closing  our  discussion  with,  the  elucidation  of  cer- 
tain general  topics  having  an  important  bearing  upon  a  right 
understanding  of  the  doctrine  of  method. 


Section  I. — Logical  Perfection  of  Thought  as  promoted 
by  proper  Definition  and  Exposition. 

Design  of  Definition  and  Exposition. 

The  design  of  definition  and  exposition  is  one  and  the  same, 
to  wit,  to  convey  to  the  mind  a,fidl,  distinct,  and  adequate  con- 
ception or  apprehension  of  the  thing  defined.  Distinctness, 
completeness,  and  precision,  are  the  essential  elements  of  every 
perfect  definition.  The  object  defined  must  be  so  presented, 
that  it  shall  stand  out  before  the  mind  with  perfect  distinctness 
as  it  is  in  itself,  and,  at  the  same  time,  with  equally  perfect 
separateness  from  all  objects  with  which  it  is  likely  to  be  con- 
founded. 

Proper  objects  of  Definition  and  Exposition. 

The  immediate  and  proper  aim  of  definition  and  exposition 
is  not  proof,  but  a  distinct  understanding  of  what  is  to  be 
proved,  and  also  of  the  terms  and  propositions  by  which  this 
end  is  to  be  attained.  These,  then,  are  the  proper  objects  of 
definition  and  exposition. 

In  entering  upon  the  elucidation  of  any  particular  subject, 
whether  it  be  some  one  entire  science,  or  some  single  part  or 


DOCTKIUE     OP     METHOD.  269 

department  of  the  same,  or  finally,  some  special  aspect  of  some 
one  subject  of  thought,  the  first  thing  to  be  accomplished  is  a 
full  and  distinct  definition  and  exposition  of  the  entire  subject, 
whatever  it  may  be,  to  be  treated  of,  and  also  of  the  end  to  be 
accomplished  in  its  elucidation  ;  so  that  that  subject  shall  stand 
out  with  perfect  distinctness  before  the  mind,  not  only  as  it  is 
in  itself,  but  separated  with  equal  distinctness  from  every  other 
subject  with  which,  in  whole  or  in  part,  it  is  likely  to  be  con- 
founded. Every  science,  for  example,  has  a  sphere  peculiar  to 
itself,  and  the  purpose  to  be  answered  by  its  elucidation  is 
equally  special  and  peculiar.  To  appreciate  the  bearing  of 
what  may  be  presented  m  the  elucidation  of  said  science,  its 
special  and  peculiar  sphere,  the  extent  and  limits  of  the  same, 
together  with  the  purpose  to  be  secured  by  its  elucidation, 
must  be  distinctly  apprehended.  To  induce  such  apprehensions 
is  the  appropriate  and  exclusive  object  of  definition  and  exposi- 
tion. 

Apply  the  same  remarks  to  the  various  terms  peculiar  to  any 
particular  treatise  or  discourse,  to  the  principles  which  lie  at 
the  foundation  of  the  same,  and  to  the  various  propositions  em- 
ployed in  the  progress  of  the  discussion,  and  we  have  a  distinct 
apprehension  of  the  proper  objects  of  definition  and  exposition, 
together  with  their  design  and  aim.  Unless  these  ends  are 
fully  accomplished,  any  real  approach  towards  logical  perfec- 
tion of  thought  is  impossible. 

Characteristics  of  all  Correct  Definitions. 

The  following,  then,  may  be  given  as  the  essential  charac- 
teristics of  all  correct  and  proper  definitions  : 

1.  That  the  definition,  considered  as  a  proposition,  is  true, 
that  is,  really  and  truly  represents  its  object,  whether  the  ob- 
ject in  itself  be  real  or  unreal.  Suppose  that  the  term  "  cen- 
taur" is  defined  as  representing  a  "  fabulous  animal — half  horse 
and  half  alligator,"  instead  of  "  half  horse  and  half  man."  The 
definition  would  be  incorrect,  not  because  that  each  being  de- 
fined is  not  equally  fabulous,  but  because  that  the  latter  defini- 


270  LOGIC. 

tion,  and  that  only,  represents  the  real  object  as  thought  by 
the  mind.  A  definition,  then,  as  a  proposition,  is  true  when  it 
represents  its  object  as  really  thought  by  the  mind,  whether 
the  object  in  itself  is  real  or  unreal,  and  this  is  an  essential  ele- 
ment of  every  correct  definition. 

2.  Not  only  must  a  definition  be  true  in  the  sense  explained, 
but  its  truth  must  be  self-evident,  so  much  so,  that  its  correct- 
ness will  not  be  a  matter  of  dispute.  Otherwise,  a  new  subject 
of  debate  arises,  which  confuses  the  mind  and  involves  in  dark- 
ness the  whole  subject  under  discussion.  This  element  of  all 
correct  definition  is  quite  too  often  overlooked,  and  that  when 
the  most  important  questions  are  involved.  Definition  is 
nothing  but  the  preparatory  means  for  discussion,  and  totally 
fails  of  its  end  when  it  itself  becomes  the  subject  of  debate. 

3.  Considered  as  a  conception  the  definition  must  be  distinct, 
that  is,  it  must  induce  in  the  mind  a  distinct  apprehension  of  its 
object  as  it  is.  The  definition  of  the  centaur  above  given,  for 
example,  has  the  first  two  characteristics.  It  wholly  lacks, 
however,  the  one  under  consideration,  for  the  reason  that  no 
one,  from  the  definition,  can  form  a  distinct  image  of  the  thing 
defined,  and  no  two  individuals  would  obtain  from  it  the  same 
conception.  Take,  in  its  place,  the  following  definition  of  the 
same  object :  "  A  centaur  is  a  fabulous  being,  half  horse  and 
half  man,"  to  wit,  a  being  whose  body  entire  is  that  of  the 
horse,  with  the  exception,  that  the  body  of  a  man  from  the 
waist  upwards  occupies  the  place  of  the  neck  and  head  of  the 
creature  referred  to.  This  definition  has  not  only  the  first  two 
characteristics  of  all  correct  definitions  above-named,  but  that 
also  under  consideration,  to  wit,  distinctness.  From  it  every 
one  will  form  a  distinct  apprehension  of  the  object  defined,  and 
all  will  obtain  the  same  apprehension.  This,  then,  is  an  essen- 
tial characteristic  of  all  correct  definitions.  The  object  must 
be  so  defined,  that  all  will  obtain  from  the  definition  a  distinct 
apprehension  of  the  object,  and  all  will  obtain  the  same  appre- 
hension. 

4.  As  a  definite  conception,  also,  the  definition  must  be  am- 
ple or  adequate,  that  is,  it  must  distinctly  represent  not  only  a 


DOCTRINE     OP     METHOD.  271 

part,  but  the  whole,  of  its  object.  Suppose,  for  example,  that 
the  term  "centaur"  represents  not  only  the  fabulous  being 
above  denned,  but  a  being  possessed  also  of  other  equally  fun- 
•damental  characteristics  not  named  in  that  definition.  In  that 
case  the  definition  would  have  the  first  three  characteristics, 
but  would  lack  another  equally  requisite  to  constitute  it  a  per- 
fect definition,  to  wit,  adequateness.  Any  definition  wanting 
in  this  one  particular  is  fundamentally  defective. 

5.  The  last  characteristic  of  every  correct  definition  that  w<> 
mention  is  determinateness,  that  is,  the  thing  defined  must 
stand  out  not  only  in  full  and  distinct  amplitude  before  the 
mind,  but  in  a  state  of  equally  determinate  separateness  from 
all  objects  with  which,  hi  whole  or  part,  it  is  likely  to  be  con- 
founded. Every  definition  is  perfect  or  imperfect  as  it  possesses 
or  wants,  in  whole  or  in  part,  all  of  the  above  characteristics. 

Characteristics  of  Defective  Definitions. 

All  definitions  are  defective  which  lack  any  of  the  characteris- 
tics above  elucidated,  and  especially  those  which  possess  the 
opposite  characteristics,  such  as  positive  incorrectness  or  doubt- 
ful correctness,  indistinctness,  want  of  completeness  or  ampli- 
tude and  of  determinateness.  A  definition  is  incorrect  when 
it  introduces  into  the  conception  or  proposition  any  elements 
not  included  in  it,  or  formally  excludes  from  it  any  which  real- 
ly belong  to  it.  Definitions  erroneous  in  one  or  the  other  of 
these  particulars  are  very  common  in  almost  all  departments  of 
thought.  Still  more  common  is  the  element  of  doubtfulness  in 
definitions.  A  definition  which  raises  a  dispute  in  regard  to  its 
own  correctness  is  fundamentally  defective. 

One  of  the  most  common  forms  of  defective,  or  rather,  per- 
haps, erroneous  definitions,  is  this — defining  a  term  or  proposi- 
tion so  as  to  involve,  by  direct  implication,  the  very  question 
at  issue  ;  an  important  form  of  "  begging  the  question." 


ELEMENTS   WHICH   ENTER   INTO,  AND   ARE   EXCLUDED   EROM,   ATT, 
PERFECT   DEFINITIONS. 

The  above,  we  judge,  will  be  universally  admitted  as  the 
essential  characteristics  of  all  perfect,  as  distinguished  from  all 
forms  of  imperfect,  definition.  We  now  advance  to  the  con- 
sideration of  another  very  important  topic  connected  with  our 
present  inquiries,  to  wit,  the  elements  which  will  enter  into, 
and  be  excluded  from,  all  perfect  forms  of  definition. 


Characteristic,  Generical,  Specifical,  and  Individual  Concep- 
tions. 

Definitions  of  characteristic  conceptions  must  designate  all 
the  elements  of  such  conceptions,  and  no  more  and  no  less. 
An  error  in  either  of  the  particulars  named  would  totally  mis- 
lead in  the  application  of  the  conception  defined.  If  any  ele- 
ment really  belonging  to  the  conception  is  omitted,  or  any  one 
not  belonging  to  it  is  included  in  it,  those  using  the  conception 
as  defined  in  testing  the  character  of  objects,  would  be  led  to 
reject  what  is  genuine  on  the  one  hand,  and  to  receive  as  such 
what  is  spurious  on  the  other. 

Similar  remarks  are  equally  applicable  to  definitions  of  ge- 
nerical conceptions,  definitions  of  ultimate  genera  especially. 
Take  any  element  from,  or  add  any  to,  a  genus,  and  it  becomes 
another  thing.  For  this  reason,  every  perfect  definition  of  a 
generical  conception  will  include  all  the  elements  of  such  con- 
ception, and  no  more  and  no  less. 

Definitions  of  specifical  conceptions  should  designate,  first, 
the  generical  conceptions  under  which  the  former  rank,  and 
then  embrace  those  elements,  and  those  only,  which  peculiarize 
and  distinguish  the  species  which  they  represent  from  other 
species  which  rank  with  them  under  the  same  genera ;  genera 
and  differentia  being  the  constituent  elements  of  species.  So 
far  as  such  definitions  include  more  or  less  than  these  elements, 
they  are  fundamentally  defective  or  erroneous. 

Definitions  of  individual  conceptions  should  designate  the 


DOCTRINE     OF     METHOD.  273 

specifical  or  generical  conceptions  under  which  the  former  as 
individuals  rank,  and  then  designate  those  properties  and  acci- 
dents, and  those  only,  by  which  such  individuals  are  distin- 
guished from  other  individuals  of  the  same  class. 


Definitions  of  Propositions. 

When  a  proposition  is  laid  down,  it  is  sometimes  necessary  to 
define  its  meaning.  In  doing  so,  it  is  most  commonly  necessary 
to  define  but  one  of  the  terms.  When  the  subject  is  known, 
and  some  attribute  is  by  the  predicate  affirmed  of  the  subject, 
then  the  former  must  be  defined — as  in  the  proposition,  "  John 
is  a  murderer."  When,  on  the  other  hand,  some  well-known 
attribute — as,  "God  is,  exists" — is  affirmed  of  the  subject,  then 
the  latter  term,  that  is,  the  subject,  will  need  to  be  denned.  If 
the  meaning  of  each  is  likely  not  to  be  understood,  then  both 
alike  will  require  definition. 

True  use  of  Affirmation  and  Negation  in  Definition. 

Terms  and  conceptions  must  often  not  only  be  affirmatively 
but  negatively  defined.  By  affirmation  we  designate  the  posi- 
tive elements  included  in  the  thing  defined.  By  negation  we 
separate  this  object  from  others  with  which  it  may  be  supposed 
to  agree  or  to  be  identical,  but  from  which  it  is  distinct,  and 
should  be  separated.  In  defining  the  crime  of  murder,  for  ex- 
ample, it  may  be  necessary  to  a  clear  and  distinct  apprehension 
of  it,  not  only  to  designate  its  essential  and  positive  characteris- 
tics, but  to  show  wherein  it  differs  from  manslaughter,  &c. 
The  former  object  is  accomplished  by  affirmation  and  the  latter 
by  negation.  Negation  should  be  employed  in  those  cases  only 
where  some  object,  really  and  essentially  different  from  that  to 
be  discussed,  is  likely  to  be  mistaken  for  it,  and  with  exclusive 
reference  to  such  object  and  the  points  of  difference  between 
such  object  and  that  to  be  defined.  It  would  throw  no  light, 
;for  example,  upon  the  crime  of  murder  to  say  that  it  is  not 
theft,  and  to  show  wherein  the  two  crimes  differ.  The  reason 
12-s 


274  logic. 

is  obvious.  The  two  forms  of  crime  are  never  confounded,  as  ia 
the  case  with  murder  and  manslaughter.  When  two  terms  are 
thus  separated,  it  is  most  commonly  necessary  to  distinctness  of 
apprehension,  not  only  to  state  the  fact  of  disagreement,  hut 
carefully  to  explain  and  elucidate  the  points  of  disagreement 
and  dissimilarity. 

Nominal  and  Real  Definitions. 

In  some  instances  we  have  occasion  merely  to  define  a  term, 
by  stating  'the  conception  which  the  former  represents.  This  is 
what  is  meant  by  the  words  nominal  definition.  In  this  case 
all  that  is  requisite  is  to  designate  the  conception,  and  then  the 
term  by  which  the  former  is  to  be  represented.  Real  defini- 
tion is  the  definition,  not  of  the  term,  but  of  the  conception  or 
thing  which  the  term  represents.  It  is  to  this  last  class  of  defi- 
nitions that  the  principles  above  elucidated  apply. 

Subjective  and  Objective  Definitions. 

In  some  instances,  also,  the  object  of  a  definition  is  to  repre- 
sent the  apprehensions  which  the  individual  presenting  it  has 
of  a  given  subject.  In  such  cases  clearness  and  distinctness  is 
all  that  others  have  a  right  to  require,  and  they  are  bound,  of 
course,  to  accept  his  own  statements  as  correctly  representing 
his  views.  This  is  what  is  denominated  subjective  definition. 
In  other  cases  the  object  is  to  represent  things  as  they  are,  or 
as  they  are  thought  by  the  general  mind.  This  is  objective 
definition.  It  is  to  this  kind  of  definition  that  the  principles 
we  have  stated  and  elucidated  apply  in  all  their  extent. 


EXAMPLES    OF   PERFECT   AND   IMPERFECT   DEFINITIONS. 

For  the  purpose  of  elucidating  still  further  the  important 
topic  under  consideration,  that  of  definition,  we  will  now  pre- 
sent a  few  miscellaneous  examples  of  perfect  and  imperfect  defi- 
nition. 


DOCTRINE     OF     METHOD. 


The  term  Judgment  defined. 


The  following  is  Kant's  definition  of  a  judgment :  "A  judg- 
ment is  the  representation  of  the  unity  of  the  consciousness  of 
various  representations,  or  the  representation  of  their  relation, 
provided  that  they  make  up  a  conception." — Kant's  Logic, 
p.  141. 

The  manifest  objection  to  this  definition  is  its  palpable  viola- 
tion of  the  author's  second  characteristic  of  a  perfect  definition, 
that,  "  as  a  conception,"  the  definition  must  be  "  distinct."  The 
definition  before  us  tends  to  but  one  result,  to  obscure  the  thing 
attempted  to  be  defined. 

"  A  judgment,"  says  President  Tappan,  "  is  an  affirmation 
of  the  mind."  The  defect  in  this  definition  is,  that  it  fails  to- 
tally to  elucidate  the  thing  to  be  defined,  the  meaning  of  the 
predicate  being  quite  as  obscure  as  that  of  the  subject,  and  as 
much  needing  definition.  Definitions  of  this  kind  are  very  com- 
mon, and  fundamentally  defective.  We  refer  to  the  practice  of 
defining  a  term  by  means  of  some  mere  synonymous  term  or 
phrase.  In  every  perfect  definition  the  predicate  is  clearly 
and  definitely  explicative  of  the  subject,  and  not  merely  its 
synonym. 

"  Judgment,"  says  Dr.  Whately,  "  is  the  comparing  together 
in  the  mind  two  of  the  notions  (or  ideas)  which  are  the  objects 
.  of  apprehension,  whether  complex  or  incomplex,  and  pronoun- 
cing that  they  agree  or  disagree  with  each  other  ;  (or  that  one 
of  them  belongs  or  does  not  belong  to  the  other)'."  Judgment, 
according  to  this  definition,  includes  two  entirely  distinct  intel- 
lectual processes — the  act  of  comparison,  and  the  "  pronouncing" 
that  the  things  compared  "  agree  or  disagree  with  each  other  ;" 
the  former  process  being  implied  by  the  latter,  but  really  and 
truly  distinct  from  it.  Now  a  judgment  is  the  mental  affirma- 
tion which  succeeds  the  act  of  comparison,  and  notning  else. 
This  definition,  therefore,  is  fundamentally  defective,  inasmuch 
as  it  includes  elements  not  found  in  the  thing  'to  be  defined. 

A  much  nearer  approach  to  perfection  is  made  in  the  defini- 
tion of  Professor  Wilson,  to  wit :  "A  judgment  is  an  act  of  the 


276  logic. 

mind  affirming  a  certain  relation  between  two  objects  of  thought 
by  means  of  their  conceptions."  The  phrase,  "by  means  of  ' 
their  conceptions,"  is  redundant  here,  and  should  constitute, 
as  it  appears  to  us,  a  part  of  the  exposition  of  a  judgment,  and  * 
not  of  its  definition.  A  perfect  definition  of  the  term  under 
consideration,  we  think,  would  be  this  :  A  judgment  is  an  act 
of  the  mind — an  act  in  which  a  certain  relation  is  affirmed  or 
denied  of  two  objects  of  thought.  It  may  then  be  shown,  by 
way  of  exposition,  that  said  affirmation  is  always,  in  fact,  made 
by  means  of  conceptions,  as  it  is  always  in  view  of  what  objects 
are  conceived  to  be,  that  is,  by  means  of  conceptions  that  we 
affirm  or  deny  any  thing  of  them.  Every  element  of  a  perfect 
definition  will  be  found  in  this  definition  as  thus  expressed  and 
expounded. 

Moral  Action  defined. 

"  A  moral  action,"  says  Dr.  Wayland,  "  is  the  voluntary  ac- 
tion of  an  intelligent  agent  who  is  capable  of  distinguishing  be- 
tween right  and  wrong,  or  of  distinguishing  what  ought  from 
what  ought  not  to  be  done."  In  reading  the  above  professed 
definition,  the  question  at  once  arises,  whether  every  voluntary 
act  of  such  an  agent  is,  in  fact,  as  is  here  directly  implied  and 
affirmed,  a  moral  act.  In  regard  to  this  question  different  and 
opposite  opinions  are  held.  We  have,  then,  in  this  case,  not  a 
proper  definition  at  all,  but  a  problematical  proposition  to  be 
investigated  and  discussed  after  a  correct  definition  has  been 
given.  Even  philosophers  have  not  generally  made  a  proper 
distinction  between  a  definition  of  an  object,  and  a  problemati- 
cal judgment  connected  with  such  object  when  defined.  A 
professed  definition,  the  truth  of  which  is  not  self-affirmed,  is 
not,  it  should  be  borne  in  mind,  a  proper  definition,  but  a  pro- 
blematical judgment  which  requires  proof. 

Let  us  now  contemplate  the  following  definition  of  a  moral 
action,  to  wit,  an  action  of  which  the  intelligence  necessarily 
affirms  that  it  ought  or  ought  not  to  be  done,  and  on  account 
of  the  doing  of  which,  merit  or  demerit  is  as  necessarily  attrib- 


^UV**r*^ 


DOCTRINE     OF     METHOD.  211 

uted  to  the  subject.  "No  one  can  possibly •  doubt,  that  if  there 
is  such  a  thing  as  a  moral  action,  these  are  its  peculiar  and 
special  characteristics — characteristics  which  clearly  distinguish 
'it  from  all  other  forms  of  action,  actual  or  conceivable.  This, 
then,  is  a  perfect  definition. 

Moral  Law  defined. 

Moral  law,  as  defined  by  Dr.  Wayland,  is  "  an  order  of  se- 
quence established  between  the  moral  quality  of  actions  and 
their  results."  Here  undeniably  is  a  fundamental  mistake  in  re- 
gard to  the  nature  of  the  thing  defined.  Moral  law  is  made  to 
be  chronologically  subsequent  to  moral  action,  whereas  the  lat- 
ter presupposes  the  former.  Moral  action  is  conformity  or  non- 
conformity to  law.  The  law  must  exist  before  the  action  is 
possible. 

"Moral  law,"  says  President  Finney,  "is  a  rule  of  moral  ac- 
tion with  sanctions."  The  author  had  just  defined  law  itself 
and  correctly  too,  as  "  a  rule  of  action."  Moral  law,  then,  must 
be  simply  and  exclusively  a  rule  of  action  of  a  peculiar  and 
special  kind.  Nothing  but  the  kind  of  action  referred  to,  aside 
from  the  idea  of  a  rule,  should  be  included  in  the  definition. 
Sanctions  attach  to  acts  of  obedience  or  disobedience  to  law, 
and  have  their  basis  in  the  merit  and  demerit  which  attach  to 
-  obedience  and  disobedience,  and  consequently  can  constitute  no 
part  of  the  law  or  rule  itself.  Then  the  phrase,  "  moral  law  is  a 
rule  of  moral  action,"  as  a  proposition,  is  really  tautological, 
moral  action  being  that  form  of  action  which  is  conformed  or 
not  conformed  to  moral  law.  The  real  meaning  of  the  propo- 
sition is,  moral  law  is  the  rule  of  conformity  or  non-conformity 
to  moral  law.  Then  the  definition  is  totally  faulty  on  the  score 
of  perspicuity,  the  phrase  "  moral  action,"  the  predicate,  need- 
ing to  be  defined  quite  as  much  as  the  subject  of  the  proposi- 
tion, the  phrase  "  moral  law." 

What,  then,  is  -a  perfect  definition  of  the  phrase  "moral 
law  ?"  We  answer  it  is  this :  Moral  law  is  that  rule  of  action 
to  which  intelligent  agents  necessarily  affirm  that  they  ought 


278  LOGIC. 

to  conform,  and  to  the  idea  of  obedience  or  disobedience  to 
which  they  as  necessarily  attach  the  idea  of  merit  or  demerit, 
that  is,  the  desert  of  good  or  ill.  Let  any  one  apply  the  testa 
of  a  perfect  definition  given  above  to  the  one  before  us,  and 
he  will  see  that  it  fully  meets  them  all.  No  one  can  fail  to  ap- 
prehend the  real  meaning  of  the  definition,  or  to  distinguish  the 
thing  defined  from  every  other  rule  of  action  actual  or  conceiv- 
able, or  to  admit  that,  if  there  is  such  a  thing  as  moral  law, 
this  is  that  rule,  and  these  are  all  the  requisites  of  a  perfect 
definition. 


A  Moral  Agent  defined. 

A  perfect  definition  of  the  phrase  "  moral  agent"  would  be 
this :  An  agent,  of  whom  we  necessarily  affirm,  that  he  ought 
to  conform  to  the  moral  law,  and  to  whom  we  necessarily  attach 
the  idea  of  the  desert  of  good  or  ill,  as  he  does  or  does  not 
conform  to  what  that  law  requires  of  him.  What  was  said  of 
the  definition  of  moral  law  is  so  manifestly  applicable  to  the 
definition  before  us,  that  we  may  safely  leave  it  to  speak  for 
itself. 

It  is  quite  common  to  define  a  moral  agent  as  one  "  who  is 
capable  of  obeying  or  disobeying  the  moral  law,"  or  as  one 
'  who  has  the  capacity  to  distinguish  what  is  right  from  what  is 
wrong,"  &c.  These,  however,  are  not  definitions  at  all,  but 
problematical  judgments  connected  with  the  idea  of  moral 
agency. 

Ultimate  Intention  defined. 

It  is  now  generally  admitted  that  every  thing  that  has  real 
moral  character  in  the  conduct  of  moral  agents  is,  in  fact,  found 
in  what  is  called  the  ultimate  intention.  The  question  which 
arises  here  is,  How  shall  this  phrase  be  defined  so  as  to  express 
and  represent  every  act  of  this  character,.that  is,  so  as  to  ex- 
press all  that,  and  that  only,  in  human  conduct  which  has  moral 
character  ?     The  importance  of  this  question  every  one  will  ad- 


DOCTRINE     OF     METHOD.  279 

mit.  Let  us  now  contemplate  a  single  example  of  a  fundamen- 
tally defective  definition  of  an  ultimate  intention.  "An  ulti- 
mate intention,"  says  President  Finney,  "  is  the  choice  of  an  ulti- 
mate end."  In  this  definition  there  are,  among  others,  the  fol- 
lowing fundamental  defects:  1.  The  predicate  of  the  proposi- 
tion is  not,  what  in  all  correct  definitions  it  is,  really  and  truly 
explicative  of  the  subject,  the  words  "  choice  of  an  ultimate 
end"  requiring  definition  just  as  much  as  the  phrase  "  an  ulti- 
mate intention."  2.  The  definition  presents  us  with  a  pro- 
blematical judgment — a  judgment  which  cannot  properly  be 
used  at  all  in  reasoning  until  its  truth  is  proven,  it  being 
doubted  and  denied  that  'all  ultimate  intentions  consist  in  tne 
choice  of  ultimate  ends.  3.  The  judgment  here  presented  is 
not,  in  fact,  true,  as  it  cannot,  according  to  the  real  meaning  of 
the  words,  be  made  to  include  any  moral  acts  or  states  relative 
to  God ;  for  neither  his  happiness  nor  moral  character  can  be 
chosen  as  an  end,  that  is,  as  something  to  be  secured  and  pro- 
moted in  the  use  of  means. 

What  then  would  be  a  correct  definition  of  an  ultimate  inten- 
tion ?  The  following,  in  our  judgment,  would  be  such  a  defini- 
tion :  All  are  aware  of  the  fact,  that  one  act  or  state  of  the  will 
may  be  determined  by,  and  thus  subordinated  to,  another  act 
or  state.  An  ultimate  intention  or  act  of  will  is  one  to  which 
others  are  or  may  be  subordinated,  and  by  which  they  are  or 
may  be  determined,  and  which  is  itself  subordinated  to,  and 
determined  by,  none  others.  On  this  definition  we  remark  : 
1.  That  no  problematical  element  enters  into  it.  2.  It  clearly 
and  adequately  designates  the  object  defined,  as  distinguished 
from  all  other  objects.  3.  It  undeniably  includes  and  desig- 
nates every  thing  in  human  action  which  can  have  a  moral  char- 
acter, and  thus  fully  answers  its  end.  We  thus  have  the  essen- 
tial characteristics  of  all  perfect'  definitions. 


The  term  God  defined. 

The  term  God  may  be  contemplated  in  two  points  of  light — 
as  representing  the  idea  of  ultimate  causation  as  held  by  all 


280  LOGIC. 

men,  whether  theists  or  anti-theists ;  and  as  representing  the 
special  theistic  hypothesis  of  such  causation.  In  the  first  sense, 
the  term  God  would  be  defined  as  the  ultimate  reason  why,  or 
determining  cause,  whatever  it  may  he,  by  which  the  facts  of 
the  universe  are  rendered  what  they  are,  and  not  otherwise. 
Even  an  atheist  would  admit  the  truth  and  correctness  of  this 
definition,  and  would  as  readily  admit  that,  as  thus  defined,  he 
himself  believes  in  God. 

As  representing  the  special  theistic  hypothesis,  the  term  God 
may  be  thus  defined :  A  self-conscious  personality  possessed  of 
all  the  attributes  involved  in  the  ideas  of  absolute  infinity  and 
perfection,  and  sustaining  to  all  conditioned  existences  the 
relation  of  unconditioned  cause.  As  representing  this  one 
hypothesis,  all  will  admit  the  truth  and  adequacy  of  this  defi- 
nition. 

We  have  given  the  above  as  simple  examples,  by  way  of 
illustration.  Every  correct  definition,  it  should  be  borne  in 
mind,  will  have,  among  others,  the  following  characteristics : 
1.  No  problematical  elements  will  be  introduced  into  the  defi- 
nition. 2.  It  will  clearly  and  adequately  represent  its  object  as 
distinguished  from  all  other  objects  of  thought.  3.  As  a  prop- 
osition, its  truth,  that  is,  the  fact  that  it  does  thus  represent  its 
object,  must  be  self-evident,  that  is,  universally  admitted.  In 
nothing  is  even  educated  mind  generally  more  deficient  than  in 
this,  the  habit  of  correct  definition,  and  almost  no  department 
of  thought  is  of  greater  importance. 


Section  II. — Promotion  op  the  Logical  Perfection  op 
Thought  by  means  of  the  Logical  Division  op  Con- 
ceptions or  Subjects. 

Terms  defined. 

Every  conception  pertains  to  its  object  as  a  whole  including 
parts.  Thus  the  conception  represented  by  the  term  mind, 
pertains  to  its  object  as  a  substance  possessed  of  the  attributes 


DOCTRINE     OP     METHOD.  281 

of  thought,  feeling,  and  voluntary  determination,  or  as  includ- 
ing the  powers  or  functions  of  intellect,  sensibility,  and  will. 
The  conception  represented  by  the  term  matter  pertains  to  its 
object,  as  possessed  of  certain  primary,  secundo-primary,  and 
secondary  qualities.  The  proper  idea  of  a  logical  division  of  a 
conception  or  subject  treated  of,  is  a  distinct  separation  of  the 
various  parts  which  constitute  the  given  whole.  The  whole, 
whether  it  be  a  generical  with  specifical  conceptions,  or  a  spe. 
cifical  with  individual  conceptions,  ranking  under  it,  or  an  indi- 
vidual conception  constituted  of  diverse  elements,  is  called  rela- 
tively to  its  parts,  the  superior,  and  its  several  parts,  the  infe- 
rior conceptions.  The  wliole  is  called,  also,  the  divided  con- 
ception, and  the  parts  the  members  of  the  division.  The  fol- 
lowing extract  from  Kant  demands  special  attention  in  this 
connection : 

"  Schol.  1. — To  dissect  a  conception,  and  to  divide  it,  are 
therefore  very  distinct  operations.  By  the  dissection  of  a  con- 
ception, we  see  what  is  contained  in  it  (by  analysis) ;  by  the 
division,  we  consider  what  is  contained  under  it.  In  this  case 
we  divide  the  sphere  of  the  conception,  not  the  conception 
itself.  The  division  is,  therefore,  so  far  from  being  a  dissection 
of  a  conception,  that  the  members  of  division  rather  contain 
more  in  them  than  the  divided  conception. 

"  Schol.  2. — We  ascend  from  inferior  to  superior  conceptions, 
and  may  afterwards  descend  from  these  to  inferior  ones,  by 
division." 


Universal  Rules  for  Logical  Division. 

We  are  now  prepared  to  state  definitely  the  universal  rules 
for  the  logical  division  of  subjects.     They  are  the  following  : 

1.  The  members  of  the  division  must  mutually  exclude  each 
other.  In  other  words,  they  must  differ  from  each  other  by 
way  of  opposition.  Things  essentially  alike  must  not  be  sepa- 
rated, nor  those  which  are  fundamentally  unlike  confounded. 
Thus  the  logical  division  of  the  mental  powers  into  intellect, 
sensibility,  will,  meets  fully  the  requirements  of  this  rule,  be- 


282  LOGIC. 

cause  each  member  of  the  division  is  fundamentally  opposed  to 
each  of  the  others.  . 

2.  The  division  must  be  complete,  that  is,  must  embrace  all 
the  parts  of  the  subject  which  are  thus  separated  from  each 
other.  The  division  of  the  mental  powers  above  stated  would 
meet  the  requirements  of  this  rule  also,  because  all  the  mental 
powers  are  there  given.  The  division  made  by  certain  philoso- 
phers, as  intellect  and  sensibility,  or  intellect  and  affections, 

•  would  meet  the  requirements  of  the  first,  while  it  would  violate 
this  rule,  the  members  of  the  division  actually  given  being  op- 
posed to  each  other,  while  one  mental  power,  the  will,  which  is 
just  as  distinct  from  the  intellect  and  sensibility  as  either  of 
these  last  is  from  the  other,  is  omitted. 

3.  Each  member  of  the  division  must  rank  under  the  whole 
— the  superior  conception — as  a  real  member  or  part  of  the 
same.  In  other  wdrds,  nothing  foreign  to  the  real  sphere  of 
the  superior  conception,  that  is,  nothing  which  does  not  really 
and  truly  rank  under  it,  must  be  introduced  into  the  division 
or  any  part  of  it.  Violations  of  this  rule,  which  is  of  funda- 
mental importance  to  the  perfection  of  logical  thinking,  are 
perfectly  common  in  almost  all  departments  of  research.  That 
which  exclusively  pertains  to  the  sphere  of  one  science  is  fre- 
quently discussed  as  a  part  of  another  and  different  one. 

4.  Taken  collectively,  the  members  of  the  division  must  fully 
make  up  or  complete  the  sphere  of  the  divided  conception,  so 
that  the  latter  shall  be  really  and  truly  given  and  be  conceived 
of,  as  a  whole  complete  in  all  its  parts.  This  rule  is  really  im- 
plied in  Rule  2,  and  is  here  given  for  the  sake  of  distinctness. 

Codivision  and  Subdivision. 

The  primary  division  of  a  conception  or  subject  into  distinct 
members  is  called  codivision.  A  similar  division  of  the  several 
parts  is  called  subdivision.  The  rules  for  the  former  are  equal- 
ly applicable  to  the  latter.  Subdivision  may  be  continued  tc 
almost  any  conceivable  extent. 


DOCTRINE     OF     METHOD.  283 

The  Fragmentary  as  opposed  to  the  Meal  Logical  Division 
of  Subjects. 

In  reference  to  every  important  department  of  thought,  the 
science  of  mind,  or  theology,  for  example,  certain  important 
and  general  questions  arise,  and'  become  the  topics  of  general 
discussion.  Suppose  that  two  individuals  attempt  to  develop 
scientific  treatises  ou  one  or  the  other  of  these  subjects.  One 
takes  up  these  several  topics  as  they  naturally  occuf  to  his 
mind,  throws  all  the  light  he  can  upon  them,  and  then  presents 
his  work  as  a  scientific  treatise  on  the  subject.  The  other  indi- 
vidual, first  of  all,  contemplates  his  subject  as  a  whole  with  ref- 
erence to  its  appropriate  and  exclusive  sphere.  It  is  then 
divided  and  subdivided  into  its  distinct  and  separate  parts  ac- 
cording to  the  fundamental  rules  of  logical  division.  The  sub- 
ject is  thus  given  as  a  whole  distinct  in  all  its  parts.  From  the 
nature  of  the  subject,  we  perceive  that  it  has  just  so  many  parts, 
and  can  have  no  more.  The  idea  of  order,  completeness,  and 
scientific  division  and  arrangement  is  completely  realized.  In 
the  first  case,  we  have  what  may  be  called  the  fragmentary, 
and  in  this  last,  the  truly  scientific  and  logical  division  of  sub- 
jects. The  former,  when  accepted  as  a  scientific  treatise,  tends 
only  to  confuse  and  darken  our  conceptions  of  the  subject  , 
treated  of. 


Section  III. — The  Promotion  of  the  Logical  Perfection 
of  Thought  by  means  of  a  proper  arrangement  of  the 
parts  of  the  subject  treated  of. 

Terms  defined — Analytic  and  Synthetic  Orders  of  Thought. 

Next  in  importance  to  a  systematic  logical  division  of  sub- 
jects is  the  order  in  which  the  members  of  the  division  should 
be  elucidated  and  arranged  relatively  to  each  other  as  parts  of 
the  whole  or  superior  conception.  A  chain  of  reasoning  stated 
in  one  order  may  be  without  logical  force  in  the  mind  of  the 
hearer,  while,  stated  in  another  order,  it  may  have  the  force  of 


demonstration.  Let  us  then  proceed  to  a  consideration  of  the 
rules  or  canons  of  order. 

Every  one  is  aware  that  in  every  department  or  subject  & 
thought  there  are  two  extremes — certain  first  principles  which 
presuppose  nothing  as  having  preceded  them,  and  upon  which 
all  that  follow  depend ;  and  certain  final  facts  or  deductions 
which  presuppose  and  depend  upon  all  that  have  gone  before, 
and  which  themselves  imply  nothing  as  following  them  ;  and 
that  between  these  extremes,  there  are  certain  intermediate 
steps  depending,  the  first  upon  the  first  truths  referred  to,  the 
next  upon  this  first  step,  and  so  on  to  the  last. 

Every  one,  also,  is  equally  aware  of  the  fact,  that  there  are 
two  distinct  and  opposite,  and  equally  valid  methods  of  treating 
subjects — the  synthetic  and  the  analytic.  The  former  begins 
with  what  is  first  in  the  logical  order,  that  is,  with  that  upon 
which  all  the  rest  primarily  depend,  and  then,  by  successive 
steps,  ascends  to  the  last  as  above  described.  The  latter  method 
begins  with  what  is  last,  that  is,  depends  logically  upon  what  has 
gone  before,  and,  by  regular  steps,  descends  to  what  is  first  in 
the  logical  order.  Of  the  synthetic  method  the  following  are 
the  universal  canons  of  order  : 

Canons  of  Order. 

1.  Place  that  first  upon  which  all  the  rest  depend,  and  which 
presupposes  nothing  as  having  preceded  it. 

2.  Place  each  intermediate  step  next  in  order  after  that 
which  it  presupposes,  and  before  all  others  which  depend 
upon  it.  * 

3.  Place  that  last  which  presupposes  all  the  rest,  and  which 
implies  none  others  as  depending  upon  it. 

4.  Where  there  are  two  or  more  intermediate  steps  which 
have  a  common  dependence  upon  something  which  precedes 
them,  and  which  do  not  depend  upon  one  another  (cases 
which  often  occur),  these  may  be  arranged  indifferently,  as 
convenience  or  taste  may  require. 

The  canons  of  order  for  the  analytic  method  are,  in  all  re- 


DOCTRINE     OF     METHOD. 


spects,  the  reverse  of  those  above  given.  Any  departures  from 
these  canons  tends  to  confuse  and  obscure  all  forms  of  logical 
thinking. 


Section   IV. — Miscellaneous    Topics    bearing    upon    our 
present  Inquiries — the  Doctrine   of   Method. 

We  now  advance  to  a  consideration  of  certain  miscellaneous 
topics  which  have  an  important  bearing  upon  our  present  inqui- 
ries— the  doctrine  of  method.  Among  the  topics  which  might 
be  considered,  we  would  invite  very  special  attention  to  the  fol- 
lowing : 

I 

characteristics  of  evert  well-conducted  argument. 

We  will  consider,  in  the  first  place,  the  essential  characteris- 
tics of  every  well-conducted  argument.  In  all  such  processes, 
the  following  leading  features  will  be,  in  a  very  special  sense, 
noticeable : 

1.  A  clear,  distinct,  and  full  presentation  of  the  real  question 
to  be  argued,  such  a  presentation  not  only  of  the  subject-matter 
of  the  question  itself,  but  an  equally  distinct  one  of  the  points  of 
distinction  between  it  and  any  one  or  more  questions  with 
which  it  is  likely  to  be  confounded  in  the  hearer  or  reader's 
mind.  A  presentation  which  leaves  any  of  these  points  obscure 
is  fundamentally  defective. 

2.  A  presentation  equally  clear  and  adequate  of  the  general 
principle  under  which  this  specific  case  ranks.  Here,  also, 
there  will  be  a  clear  and  distinct  statement,  not  only  of  the  na- 
ture of  the  principle  as  it  is  in  itself,  but  as  it  stands  distin- 
guished from  every  other  principle  with  which  it  may  be  likely 
to  be  confounded. 

3.  A  corresponding  exhibition  of  the  evidence  in  favor  of  the 
reality  of  the  facts  (if  these  are  not  admitted)  bearing  upon  the 
case  at  issue. 

4.  A  similar  presentation  of  the  real  bearing  of  these  facts 


286  logic. 

upon  this  one  question,  and  in  opposition  to  every  other  contra- 
dictory or  opposite  hypothesis. 

5.  An  exhibition  of  the  same  character,  of  the  nature  and  real 
bearing  of  any  objections  which  may  be  urged  against  this  hy- 
pothesis, and  of  any  arguments  adduced  in  favor  of  any  contra- 
dictory or  opposite  hypothesis.  Not  to  give  an  objection  as  it 
is,  and  not  to  meet  it  in  all  its  force,  is,  in  fact,  an  admission  of 
its  validity,  and  of  the  corresponding  weakness  of  the  hypothe- 
sis against  which  said  objection  is  adduced. 

Note  1. — In  reasoning,  strictly  and  absolutely  demonstrative, 
there  is  seldom,  if  ever,  any  occasion  to  answer  objections,  or 
to  consider  the  bearing  of  evidence  against  any  hypothesis  con- 
tradictory or  opposite  to  that  actually  established,  inasmuch  as 
no  valid  objections  can  possibly  he  against  a  conclusion  thus  es- 
tablished, and  all  opposite  and  contradictory  propositions  must 
of  course  be  false. 

Note  2. — The  order  in  which  the  different  departments  of 
any  subject  shall  be  presented  depends  upon  circumstances. 
The  design  of  the  above  statements  is  to  give  the  characteris- 
tics of  aU  well-conducted  processes  of  reasoning,  without  giving 
the  order  in  which  those  characteristics  shall  appear. 

Methods  of  Proof — the  Direct  and  Indirect,  and  the  two 
united  in  the  same  * 


The  subject  which  next  claims  our  attention  is  the  different 
methods  of  proving  a  proposition.  Of  these  there  can  be  but 
three — the  direct,  in  which  the  weight  of  evidence  is  brought 
to  bear  immediately  and  directly  in  favor  of  the  fact,  that  the 
conclusion  is  or  must  be  true  ;  the  indirect,  in  which  it  is  shown 
that  the  contrary  or  contradictory  of  the  given  proposition  is  or 
must  be  false,  and  from  hence  the  truth  of  the  latter  is  imme- 
diately inferred  ;  and  cases  in  which  both  methods  are  brought 
to  bear  in  favor  of  the  proposition  to  be  proven. 

Some  propositions  admit  of  proof  in  the  first  form  only,  some 
in  the  second,  and  some  equally  by  both  united.  Nothing  but 
good  sense  and  the  habit  of  careful  reflection  can  decide  which 


DOCTRINE     OF     METHOD.  287 

form  of  proof  should  be  used  on  any  given  occasion.  For 
example,  let  us  suppose  that  the  proposition  to  be  argued  is 
this,  that  God  is  good.  The  common  method  of  arguing  this 
question  is,  first  to  adduce  the  positive  evidence  of  the  Divine 
goodness,  and  then  to  answer  objections  which  may  be  urged 
against  it.  Now  the  argument  would  be  rendered  incompara- 
bly more  forcible  and  conclusive,  if  the  difficulties  and  objec- 
tions in  regard  to  the  opposite  proposition  were  also  set  with 
full  distinctness  before  the  mind. 


CHARACTERISTICS    OF,  ALL  FORMS   OF  VALID   EVIDENCE. 

Valid  evidence  will  always  be  of  a,  positive  character,  that  is, 
it  will  always  positively  affirm  or  deny  some  given  proposition. 
It  may  affirm  the  proposition  as  certainly  or  uncertainly,  as 
probably  or  improbably,  as  possibly  Tor  impossibly,  true  or 
false,  &c.  Whatever  the  form  of  the  affirmation  may  be,  this 
will  be  its  fundamental  characteristic.  Evidence  not  positive, 
which  does  not  positively  affirm  or  deny,  that  is,  evidence  equal- 
ly consistent  with  two  or  more  contradictory  hypotheses,  is  of 
no  account  whatever  in  the  matter  of  proof. 

In  all  well-conducted  arguments,  we  would  also  remark,  the 
hind  of  proposition  to  be  established,  that  is,  whether  it  is  to  be 
proven  as  certainly,  probably,  or  possibly  true,  will  always  be 
distinctly  stated,  together  with  the  specific  nature  and  bearing 
of  the  evidence  to  be  presented. 

FORMS    OF   EVIDENCE   CLASSIFIED. 

Evidence  adduced  to  prove  the  reality  of  facts  (testimony, 
for  example),  or  the  truth  of  particular  propositions,  belongs  in 
all  its  forms  to  one  or  the  other  of  the  three  following  classes  : 
1.  Evidence  which  never  deceives  or  misleads.  2.  Evidence 
wholly  unreliable  or  wholly  indecisive.  3.  Forms  of  evidence 
lying  between  these  two  classes,  and  partaking  more  or  less  of 
the  characteristics  of  the  two.  There  are  statements,  as  we  all 
know,  which  all  who  are  acquainted  with  the  facts  of  the  case 


288  LOGIC. 

no  more  doubt,  and  can  no  more  doubt,  than  they  do  or  can 
any  of  the  conclusions  reached  in  the  mathematics ;  such  state- 
ments, for  example,  as  these,  that  there  are  such  cities  as  London 
and  Paris  ;  that  Bonaparte  was  defeated  at  Waterloo,  &c.  The 
reason  is,  that  such  statements  are  sustained  by  a  kind  of  evi- 
dence which  all  men  know,  and  can  but  know,  never  does,  in 
fact,  mislead.  There  are  statements,  on  the  other  hand,  the 
truth  of  which,  by  the  evidence  which  stands  around  them,  is 
wholly  a  matter  of  doubt.  There  is  still  another  class  of  state- 
ments which  command  our  belief  in  various  degrees.  In  all 
reasoning  from  facts,  these  characteristics  of  evidence  in  its  va- 
rious forms  should  be  kept  distinctly  in  mind,  and  in  each  given 
case  the  specific  nature  of  the  evidence  bearing  upon  it  should 
be  the  object  of  distinct  apprehension.  In  "Leslie's  Short 
Method  with  Deists,"  the  characteristics  of  historical  evidence 
of  the  first  class  are  very  distinctly  stated. 

CHARACTERISTICS    OF   ALL   FORMS    OF   VALID   PROOF. 

The  forms  of  proof  are  various,  according  to  the  nature  of 
the  propositions  to  be  proven,  and  the  nature  of  the  evidence 
by  which  they  are,  or  are  attempted  to  be,  proven.  Among 
these  forms  we  notice  particularly  the  following  : 

The  Mathematical. 

Mathematical  proof,  commonly  called  by  way  of  eminence, 
the  demonstrative,  has  in  all  cases  the  following  characteris- 
tics, to  wit:  1.  The  terms,  the  two  extremes  and  the  middle, 
will  be  absolutely  definite  in  their  meaning,  and  that  meaning 
equally  intelligible  and  known.  2.  In  affirmative  conclusions 
the  extremes  will  be  given,  both  alike,- as  absolutely  agreeing 
with  the  middle  term.  3.  In  negative  conclusions  one  extreme 
will  be  given  as  agreeing,  and  the  other  as  disagreeing,  abso- 
lutely with  the  middle  term.  4.  When  the  conclusions  are 
universal,  such  must  be  the  relations  of  both  extremes  to  the 
middle  term,  and  in  particular  conclusions  one  extreme  must 


DOCTRINE     OF     METHOD.  289 

be  related  universally,  and  the  other  not  so,  to  the  middle  term. 
This  last  characteristic  belongs  properly  to  a  previous  depart- 
ment of  our  subject,  and  is  repeated  here  only  for  the  sake  of 
distinctness. 


Reasoning  from  Facts  to  General  Conclusions,  or  from  one 
Fact  to  a?iother. 

When  reasoning  is  not  mathematical,  as  when  we  reason 
from  effects  to  causes,  from  facts  to  general  laws,  acts  to  mo- 
tives, phenomena  or  qualities  to  substances,  or  from  facts  (testi- 
mony, for  example)  to  othef  facts,  &c,  the  following  will  be 
the  characteristics  of  all  valid  proof:  1.  The  facts  adduced 
must  not  only  be  real,  but  pertain  really  and  truly  to  the  sub- 
ject to  which  they  are  referred.  2.  They  must  all  consist  with, 
that  is,  none  of  them  must  contradict,  the  hypothesis,  to  prove 
which  they  are  adduced.  3.  They  must  undeniably  be  irrecon- 
cilable with  any  conceivable  hypothesis  but  this  one  exclusive- 
ly. 4.  This  one  hypothesis  they  must  as  clearly  affirm.  Some- 
times a  class  of  facts  may  be  reconcilable  with  no  known,  or  at 
present  conceivable,  hypothesis,  but  one,  and  with  this  they 
may  all  harmonize.  Yet  such  may  be  their  nature,  that  they 
do  not  certainly  affirm  this  hypothesis  as  true.  In  such  cases 
the  facts  really  stand  unexplained,  this  one  hypothesis  having 

;  the  preference  to  any  other  now  known.  Any  of  these  forms 
of  proof  wanting  any  of  these  characteristics  must  be  held  as  in- 
valid, and  all  possessing  these  as  valid.     In  all  well-conducted 

:  arguments  the  evidence  adduced  will  be  shown  in  fact,  if  not  in 
form,  to  possess  the  above  characteristics. 


THE   TRUE    AND    PROPER    METHOD    OP   DETERMINING    THE    CHAR- 
ACTER  AND   VALIDITY    OF   ANY    GIVEN   ARGUMENT. 

The  question  which  next  claims  our  attention  is  the  true  and 
proper  method  of  examining  any  given  argument,  for  the  pur- 
pose of  determining  its  validity.  The  following  we  lay  down 
as  the  most  essential  elements  of  such  a  process  : 


290  LOGIC. 

1.  First  of  all,  attention  should  be  directed  to  the  terms  or 
conceptions  employed  in  the  argument,  and  these  should  be 
carefully  examined  in  the  light  of  such  questions  as  the  follow- 
ing :  (l.)  What  is  the  real  meaning  of  said  terms,  and  what 
is  implied  in  them  ?  (2.)  Are  the  conceptions  represented  by 
said  terms  valid,  that  is,  do  they  correctly  represent  their  ob- 
jects ?  or,  is  the  whole  argument  based  upon  a  misconception 
of  said  objects  ?  (3.)  Are  these  terms  employed  throughout 
in  the  same  sense  ?  or  do  they,  in  different  parts  of  the  pro- 
cess, represent  different  conceptions  ?  A  failure  in  either  of 
these  fundamental  particulars  would  vitiate  the  whole  argu- 
ment. 

2.  The  next  object  of  attention  is  the  major  premise,  provid- 
ed it  is  a  general  principle  assumed  as  self-evidently  true.  This 
principle  should  always  be  examined  in  the  light  of  such  ques- 
tions as  the  following:  (l.)  What  is  the  real  meaning  of  this 
principle,  and  what  is  implied  in  it  ?  (2.)  What  is  its  real  char- 
acter, that  is,  is  it  in  fact  a  first  truth,  or  a  mere  problematical 
judgment  requiring  proof?  (3.)  Is  the  proposition  true  in  the 
form  in  which  it  is  here  given  ?  It  is  not  unfrequently  the 
fact  that  a  principle  which  is  true  in  one  form,  is  given  in 
another  and  different  form,  a  form  in  which  it  is  not  true. 

8.  The  inquiry  next  in  order  pertains  to  the  character  and 
bearings  of  the  facts  which  are  arranged  under  a  general  prin- 
ciple, an  inquiry  which  should  always  take  the  following  di- 
rection :  (1.)  Are  these  facts  real,  that  is,  are  they  affirmed  as 
such  by  valid  evidence  ?  (2.)  Do  they  really  belong  to  the  \ 
class  to  which  they  are  referred  ?  Facts  referred  to  the  crime 
of  murder,  for  example,  may  have  the  exclusive  characteristics 
of  some  other  class  of  acts,  such  as  manslaughter,  or  justifiable 
homicide  ;  or  they  may  have  the  common  characteristics  of  the 
three,  that  is,  be  equally  consistent  with  each  and  all  alike,  and 
hence  affirm  neither  in  distinction  from  the  other.  Facts  can- 
not logically  be  referred  to  any  given  class,  unless  they  bear  the 
exclusive  characteristics  of  said  class  ;  that  is,  they  do  not  prove 
any  one  hypothesis,  unless  they  contradict  every  contradictory 
and  opposite  hypothesis. 


DOCTRINE     OF     METHOD.  291 

4.  The  last  object  of  special  attention  will  be  the  relations 
between  the  premises  and  conclusion,  as  to  whether  the  latter, 
both  in  respect  to  its  matter  and  form,  does  or  does  not  result 
from  the  former. 

Example  in  illustration. 

In  illustration  of  the  manner  of  applying  the  above  principles 
we  will  take  a  single  example,  the  theistic  syllogism  as  stated 
by  Professor  Tulloch  in  his  "prize  essay"  entitled  "Theism." 
"  The  theistic  argument,"  he  says,  "  may  be  syllogistically  ex- 
pressed as  follows,  in  a  form  which  appears  to  us  at  once  sim- 
ple and  free  from  ambiguity,  viz. : 
First  or  major  premise, 

Order  universally  proves  mind  ; 
Second  or  minor  premise, 

The  works  of  nature  discover  order  ; 
Conclusion, 

The  works  of  nature  prove  mind." 

In  examining  the  above  argument  it  will  be  perceived  at 
once,  that  as  far  as  the  terms  employed  are  concerned,  to  wit, 
"  order,"  "  mind,"  and  "  the  works  of  nature,"  every  condition 
required  is  fulfilled.  No  doubt  does  or  can  exist  in  respect  to 
their  meaning  or  validity. 

Let  us  then  turn  our  attention  to  the  major  premise,  "  Order 
universally  proves  mind."  The  meaning  of  this  proposition 
is  undeniably  this — Order,  whatever  its  nature  or  character, 
whether  it  is  mental  or  physical,  proves  mind  as  its  originating 
cause.  In  other  words,  order,  whenever  and  in  whatever  form 
it  appears,  exists  exclusively  as  an  effect,  and  owes  its  existence 
to  mind  as  its  originating  cause.  Such,  undeniably,  is  the  real 
meaning  of  this  proposition.  What  is  its  character  ?  Is  it  a 
first  truth,  that  is,  is  its  truth  self-evident  ?  Or  is  it  a  pro- 
blematical proposition  which,  if  true,  needs  proof?  That  its 
truth  is  not  self-evident  our  author  himself  admits,  and  all  must 


5292  LOGIC. 

admit,  from  the  fact,  also,  that  its  validity  is  denied  hy  all  who 
deny  the  claims  of  theism. 

Then  is  this  proposition  true  in  fact  ?  To  prove  that  it  is  not, 
we  have  only  to  adduce  a  single  example  of  order,  which  is  not 
an  effect  of  any  cause  whatever,  and  which,  consequently,  does 
not  owe  its  existence  to  mind  as  its  originating  cause.  Such  an 
example  we  do  have  in  the  Divine  mind.  Here  is  order  in  ab- 
solute perfection,  order  which  is  not  an  effect  of  any  cause 
whatever,  and  therefore  does  not  prove  mind  as  its  originating 
cause.  Whether  we  affirm  or  deny  the  Divine  existence,  also, 
one  thing  is  undeniable,  to  wit,  that  the  principle  of  order  in 
the  universe,  whatever  its  nature  may  be — a  principle  which  is 
itself  the  highest  example  of  order — is  not  an  effect  of  any 
cause,  and  consequently  does  not  prove  mind  in  the  sense  in 
which  order  is  affirmed  to  prove  it  in  the  proposition  before  us. 
The  proposition,  then,  in  the  form  in  which  it  is  here  stated,  is 
not  true,  and  we  have  a  fundamentally  erroneous  statement  of 
the  theistic  argument.  This  argument  syllogistically  stated  in 
its  true  form  would  stand  thus  : 

Order,  which  once  did  not  exist  and  began  to  be,  that  is,  order  which  is  an 

effect  originated  in  time,  proves  mind  ; 
The  order  discovered  by  the  works  of  nature  is  of  this  exclusive  character  ; 
The  works  of  nature,  therefore,  prove  mind. 

No  one  who  rightly  apprehends  the  meaning  of  the  major 
premise  in  this  syllogism  will  doubt  its  validity.  The  only  dif- 
fer-ence  of  opinion  which  can  arise  will  pertain  to  the  validity  of 
the  minor  premise ;  and  this  must  be  the  character  of  every  • 
scientific  argument  whose  major  premise  is  a  general  principle. 
Said  premise  must  be  an  admitted  truth,  and  the  only  question 
on  which  issue  shall  be  joined,  as  far  as  the  premises  are  con- 
cerned, must  be  the  validity  of  the  minor  premise.  We  shall 
have  occasion  to  allude  to  this  subject  again  in  another  con- 
nection. We  allude  to  it  now  for  the  exclusive  purpose  of 
elucidating  the  -proper  method  of  examining  any  given  argu- 
ment. 

In  regard  to  the  minor  premise  and  conclusion  of  Professor 


DOClfilNE     OP     METHOD.  293 

Tulloch's  syllogism,  every  condition  required  is  perfectly  ful- 
filled. This  fact  is  too  evident  to  require  any  further  eluci- 
dation. 

METHOD  OR  FORMS  OF  PROVING  ANY  GIVEN  PROPOSITION  FALSE. 

The  inquiry  to  which  we  next  advance  is,  the  method  or 
forms  in  which  any  given  proposition  which  is  false  may  be 
proved  to  be  such.     They  are  the  following  : 

1.  In  case  it  is  a  universal  proposition,  proving  its  contrary  to 
be  true.  The  proposition  is  then  proved  to  be  false  in  all  its 
extent.  » 

2.  Proving  its  contradictory  to  be  true.  In  this  case,  if  the 
proposition  is  a  particular  one,  it  is  proven  false  in  all  its  ex- 
tent ;  if  it  is  a  universal  proposition,  it  is  proven  false  in  that 
form. 

3.  By  showing  it  to  be  self -contradictory .  No  such  proposi- 
tion can,  by  any  possibility,  be  true. 

4.  By  proving  that  its  truth  is  incompatible  with  some  other 
proposition  known  to  be  true.  Thus  in  law,  an  alibi  undeniably 
established,  absolutely  disproves  any  crime  charged  upon  an  in- 
dividual, the  fact  of  his  being  in  one  place  at  the  time,  being 
incompatible  with  the  truth  of  the  charge  referred  to. 

Some  propositions  may  be  proven  false  in  one  form  and  some 
in  another,  and  success  in  such  efforts  often  depends  wholly 
upon  a  clear  discernment  of  the  form  demanded  in  the  particu- 
lar case  under  discussion,  and  the  direction  of  the  entire  argu- 
ment upon  that  one  point.  How  often,  for  example,  is  utterly 
useless  and  hopeless  labor  expended  in  an  attempt  to  prove  the 
opposite  of  a  universal  proposition,  when  nothing  is  required 
in  the  circumstances  but  the  proof  of  its  contradictory,  the  lat- 
ter being  of  very  easy  accomplishment,  and  the  former  equally 
difficult  if  not  impossible. 
I 


METHOD   OR  FORMS   OF   REFUTING   ANY   GIVEN  ARGUMENT. 

Term  defined. 

Refutation  and  disproof  are  totally  different  things.  In  the 
latter  process  the  object  is  to  prove  a  proposition  untrue.  In  the 
former  the  object  is  to  show,  that  a  proposition  is  not,  in  fact, 
proven  by  the  arguments  adduced  to  prove  it.  Refutation  may 
be  complete  and  perfect,  and  the  proposition  referred  to  be  true 
notwithstanding.  Different  arguments  admit  of  refutation  in 
one  or  the  other  of  the  following  forms,  and  any  given  argu- 
ment having  any  of  these  defects  is  void  of  logical  consequence  : 

1.  Some  processes  of  argumentation  are  based  upon  essential 
misconceptions  of  the  subject-matter  under  discussion.  This 
fact  being  shown,  the  logical  inconclusiveness  of  the  whole  pro- 
cess is  undeniably  established,  and  nothing  further  in  the  form 
of  refutation  is  demanded. 

2.  Other  processes  are  defective  in  respect  to  the  general 
principle  on  which  they  rest,  and  may  be  refuted  by  disclosing 
this  defect.  For  example,  (l.)  Such  principle  may  be  false  in 
fact.  (2.)  It  may  be  false  in  the  form  in  which  it  is  presented 
in  the  argument,  as  in  the  case  which  we  considered  as  illus- 
trative of  the  proper  method  of  examining  arguments.  (3.)  It 
may  be  irrelevant  to  the  subject,  and  hence,  though  true  in 
itself,  may  not  involve  the  conclusion  deduced  from  it. 

3.  Other  processes  are  defective  in  respect  to  the  matters  of 
fact  which  are  adduced  as  coming  under  the  principle  referred 
to,  and  the  argument  based  upon  this  principle  may  be  refuted 
by  showing  this  defect,  (l.)  The  statement  of  facts  may  be 
untrue.  (2.)  Those  statements  may  not  be  sustained  by  valid 
evidence.  (3.)  They  may  not  belong  to  the  principle  or  class 
to  which  they  are  referred,  or  may  have  the  essential  charac- 
teiistics  of  another  and  different  class.  (4.)  They  may  not  be 
decisive  at  all,  that  is,  they  may  be  equally  consistent  wTith  dif- 
ferent and  opposite  hypotheses.  No  specific  crime,  for  exam- 
ple, can  be  proven  by  facts  which  may  be  performed  by  per- 
sons perfectly  innocent.     An  argument  having  any  of  these  de- 


DOCTRINE     OF     METHOD.  295 

fects  is  void  of  logical  consequence,  and  is  perfectly  refuted 
when  any  one  of  them  is  shown  to  be  involved  in  it. 

4.  Other  processes,  we  remark  finally,  are  defective  for  the 
want  of  logical  connection  between  the  premises  and  conclusion. 
When  such  want  is  shown -in  any  given  case,  the  refutation  is 
complete. 

In  all  cases  of  refutation  the  first  step  is  a  distinct  determina- 
tion of  the  precise  form  of  the  defect  in  the  specific  case  under 
consideration.  Effort  should  then  be  concentrated  upon  that 
particular  point.  Some  processes  are  faulty  in  one  particular 
and  some  in  another,  and  some  in  most  if  not  all  respects.  Ar- 
guments perfectly  void  of  logical  consequence  not  unfrequently 
appear  impregnable,  because  their  impregnable  instead  of  their 
really  weak  points  are  assailed. 

OBJECTIONS   TO   A   GIVEN   HYPOTHESIS   WHEN  VALID. 

Against  almost  every  hypothesis  on  almost  any  subject  not 
falling  within  the  sphere  of  absolute  demonstration,  very  plausi- 
ble objections  may  be  urged.  Hence  a  very  important  inquiry 
arises,  to  wit,  when  shall  an  objection  to  any  given  hypothesis 
be  considered  as  valid,  that  is,  as  conclusive  against  the  truth 
of  said  hypothesis  ?  All  such  objections  will  have  the  following 
characteristics : 

1.  The  facts  implied  in  the  objection  must  be  real,  that  is, 
must  be  affirmed  as  such  by  really  valid  evidence. 

2.  The  reality  of  said  facts  must  be  incompatible,  and  unde- 
niably so,  with  the  truth  of  said  hypothesis.  It  must  not  pre- 
sent a  mere  difficulty,  one  which  we  may  not  now  know  how  to 
explain  consistently  with  said  hypothesis,  but  one  which  unde- 
niably cannot  be  thus  explained.  A  difficulty,  it  should  be 
borne  in  mind,  is  one  thing ;  real  incompatibility  is  quite  another. 
Facts  difficult  or  unsusceptible  of  explanation  in  our  present 
state  of  knowledge  may  be  urged  against  hypotheses  undenia- 
bly true.  An  objection  to  be  valid  must  present  a  difficulty  of 
this  kind,  that  the  fact  which  it  asserts  must  be  unreal,  or  the 
hypothesis  against  which  it  is  urged  must  be  false.     Against  the 


296  logic. 

hypothesis  of  the  identity  of  the  nervous  fluid  and  electricity, 
for  example,  this  objection  is  urged,  to  wit,  that  the  latter  will, 
and  the  former  will  not,  in  fact,  pass  along  the  nerve  when  it  is 
tightly  hound  with  a  cord.  Here  is  a  fact  affirmed  which  is  not 
merely  difficult  of  explanation  in  consistency  with  said  hypothe- 
sis, but  strictly  and  undeniably  incompatible  with  it.  Either 
the  fact  asserted  is  unreal,  or  the  hypothesis  must  be  false. 
This  is  the  exclusive  character  of  all  valid  objections  against 
any  hypothesis. 

Note  1. — Every  one  who  urges  any  particular  objection 
against  any  hypothesis  should  be  required,  before  an  answer  is 
attempted,  to  prove  that  the  fact  he  asserts  is  real,  and  then, 
that  if  it  is  true,  the  hypothesis  against  which  it  is  urged  must 
be  false.  That  is  the  burden  of  proof  resting  upon  the  ob- 
jector. 

Note  2. — Individuals  in  treating  objections  frequently  err  in 
two  important  particulars — not  distinguishing  in  the  first  place 
between  a  fact  difficult  of  explanation,  and  one  incompatible 
with  the  hypothesis  against  which  it  is  urged ;  and  in  the  next, 
instead  of  requiring  the  objector  to  prove  his  facts,  and  show 
that  they  possess  the  element  of  real  incompatibility,  they  as- 
sume the  burden  of  explaining  all  difficulties,  thus  practically 
admitting  that  unless  their  hypothesis  is  totally  free  from  diffi- 
culties it  cannot  be  true. 


METHOD    OP    REFUTING    OBJECTIONS,    OK    THE    FORMS    IN   WHICH 
THEY   MAY   BE   REFUTED. 

One  more  topic  demands  our  special  attention,  to  wit,  the 
proper  method  or  forms  of  refuting  objections.  An  invalid  ob- 
jection may  be  shown  to  be  such  in  one  or  the  other  of  the  fol- 
lowing forms,  or  by  more  or  less  of  them  combined  : 

1.  It  may  be  shown  that  the  objection  is  based  upon  a  funda- 
mental misconception  of  the  subject  against  which  it  is  urged. 

2.  It  may  be  shown  that  the  fact  presented  in  the  objection 
is  unreal,  or  wants  valid  evidence  of  being  real. 


DOCTRINE     OF     METHOD.  297 

3.  That  the  fact,  if  admitted,  presents  a  mere  difficulty,  and 
wholly  lacks  the  element  of  incompatibility. 

4.  That  precisely  the  same  or  similar  objections  lie  against 
the  opposite  hypothesis,  when  one  of  the  two  must  be  true. 
That  objection  cannot  be  valid  which  would,  as  in  such  a  case, 
exist  in  all  its  force,  if  the  hypothesis  against  which  it  is  urged 
were  true. 

5.  That  the  same  or  precisely  similar  objections  he  against 
hypotheses  known  and  admitted  to  be  true.  Such  objections 
must  be  void  of  validity,  of  course.  "  Butler's  Analogy"  may 
be  referred  to  as  an  example  of  this  form  of  refuting  objec- 
tions. 

13« 


PART  IV. 

APPLIED    L  OGIC. 


Our  object  in  this,  the  last  department  of  our  present  inves- 
tigations, is  an  illustration  of  the  principles  which  we  have  al- 
ready presented  by  applying  said  principles  to  a  number  of  spe- 
cific cases  in  the  various  departments  of  thought  and  inquiry. 
As  our  exclusive  object,  as  far  as  the  science  of  logic  is  con- 
cerned, is  illustration,  the  examples  selected  will  be  wholly  of  a 
miscellaneous  character,  with  no  special  reference  to  scientific 
arrangement. 

The  Anglo-Saxon  and  German  Methods  of  developing 
Thought. 

We  have  already  distinguished  between  the  fragmentary  and 
scientific  methods  of  developing  thought,  the  former  consisting 
in  a  mere  aggregation  of  topics  generally  contemplated  and 
discussed  in  connection  with  some  one  department  of  thought 
and  investigation,  and  the  latter  in  a  systematic  development 
of  said  department  itself  in  accordance  with  the  immutable  laws 
and  principles  of  scientific  definition,  and  logical  division  and 
arrangement  of  topics.  As  far  as  method,  in  the  development 
of  thought,  is  concerned,  the  productions  of  the  German  mind 
pre-eminently  bear  the  characteristics  of  scientific  development, 
while  those  of  the  Anglo-Saxon  partake,  to  a  very  great  extent, 
of  the  fragmentary.  Each  department  of  thought  is  developed 
by  the  German  mind  from  a  certain  "  stand-point,"  and  is  so 


APPLIED     LOGIC.  299 

developed  that  every  particular  topic  is  distinctly  presented  as 
a  necessary  part  of  an  all-comprehending  whole,  thus  distinctly 
realizing  the  idea  of  system.  In  treatises  proceeding  from  the 
Anglo-Saxon  mind,  on  the  other  hand,  we  too  often  meet  with 
little  more  than  an  aggregation  of  topics  falling  within  the 
sphere  of  the  department  of  thought  to  he  developed,  while 
each  topic  is  developed  with  little  reference  to  the  idea  of  a 
whole  including  its  parts. 

Reasons  for  this  difference. 

The  reasons  for  this  diversity* are  obvious.  In  the  German 
mind,  under  the  influence  of  the  philosophy  of  Kant,  the  d 
priori  element  of  thought  is  very  distinctly,  while  in  the  An- 
glo-Saxon mind,  in  consequence  of  that  of  Locke,  it  is  very  in- 
distinctly, developed.  Methods  of  thinking  which  distinctly 
repudiate,  as  the  philosophy  of  Locke  does,  all  elements  of 
thought  hut  those  immediately  derived  from  experience — those 
immediately  given  by  external  and  internal  perception  (sense 
and  consciousness) — can  have  little  else  than  a  fragmentary 
character,  while  those  which  not  only  recognize  the  facts  of  ex- 
perience but  also  their  logical  antecedents — the  d  priori  ele- 
ments of  thoughts — and  are  developed  with  distinct  reference  to 
the  latter,  the  ideas  of  substance,  cause,  and  of  a  whole  includ- 
ing parts,  &c,  must  almost  of  necessity  assume  the  form  of  sys- 
tematic and  scientific  logical  development.  The  above  state- 
ments present  a  distinct  view  of  what  the  philosophy  of  Locke 
has  done  for  the  Anglo-Saxon,  on  the  one  hand,  and  what  that 
of  Kant  has  done  for  the  German  mind,  on  the  other. 

Illustration  1. — Systems  of  Natural  Theology  developed  ac- 
cording to  these  two  Methods. 

We  will  elucidate  the  principles  above  stated  by  two  exam- 
ples. The  first  is  a  view  of  systems  of  natural  theology  de- 
veloped according  to  these  two  opposite  methods. 

According  to  the  fragmentary  method,  writers,  for  the  most 


300  LOGIC. 

part,  commence  with  an  attempted  demonstration  of  the  propo- 
sition, "  God  exists,"  and  this  without  any  specific  definition  of 
the  term  God.  Then,  hy  an  independent  process  of  deduction, 
there  is  an  attempted  proof  of  the  fact,  that  God  possesses  cer- 
tain attributes,  such  as  spirituality,  omnipotence,  omniscience, 
omnipresence,  goodness,  &c.  In  all  such  cases  as  these,  it  will 
be  perceived  at  once,  that  we  have  a  mere  aggregation  of  topics 
generally  considered  as  connected  with  the  subject  before  us, 
while  there  is  the  total  absence  of  system  scientifically  consid- 
ered. The  parts  have  no  principles  of  necessary  connection, 
and  hence  do  not  appear  as  necessary  parts  of  a  given  whole, 
parts  separated  and  united  according  to  the  necessary  laws  of 
logical  division  and  arrangement. 

According  to  the  scientific  method,  first  of  all,  the  term  God 
would  be  defined  as  representing  a  self-conscious  personality 
endowed  with  all  the  attributes  involved  in  the  ideas  of  abso- 
lute infinity  and  perfection,  and  sustaining  to  all  conditional  ex- 
istences the  relation  of  unconditioned  cause.  Then  the  proposi- 
tion, "  God  exists,"  God,  as  representing  such  an  idea,  would  be 
demonstrated.  The  next  inquiry  would  be,  what  attributes  are 
necessarily  supposed  by  such  an  idea  of  God,  and  in  what  form 
shall  such  attributes  be  affirmed  of  him  ?  The  number  of  attri- 
butes and  the  form  of  each  would  be  determined  by  this  one 
idea,  and  elucidated  in  the  light  of  the  same.  Here  we  have 
realized  the  idea  of  system,  and  no  treatise  developed  upon  op- 
posite principles  deserves  the  name  of  system.  Hitherto  the 
fragmentary  method  has  almost  exclusively  obtained  in  the 
science  of  theology. 

Illustration  2. — Systems  of  Intellectual  Philosophy  devel- 
oped according  to  these  two  Methods. 

We  will,  in  the  next  place,  contemplate  systems  of  intellectual 
philosophy  developed  according  to  these  two  distinct  and  oppo- 
site methods.  In  developing  a  system  in  accordance  with  the 
truly  systematic  or  scientific  idea,  the  first  aim  would  be  to  de- 
termine definitely  the  sphere  of  the  science  referred  to.     In  ac- 


APPLIED     LOGIC.  30] 

complishing  this  object  the  threefold  distinction  will  be  made 
between  the  mental  faculties,  as  consisting  of  the  intellect,  to 
which  all  the  phenomena  of  thought  are  referred  ;  the  sensibili- 
ty, to  which  are  referred  all  sensitive  states  or  feelings,  such  as 
sensations,  emotions,  desires,  &c. ;  and  the  will,  to  which  per- 
tains all  mental  determinations.  The  object  or  sphere  of  the 
science  of  intellectual  philosophy  will  then  be  defined  as  consist- 
ing in  this — a  development  of  the  functions  and  laws  of  the 
human  intelligence  or  intellect.  In  entering  upon  this  depart- 
ment of  inquiry,  all  intellectual  operations  will  be  divided  into 
two  classes,  the  primary  and  secondary — the  former  furnishing 
us  with  all  the  original  elements  of  thought,  and  the  latter  con- 
sisting of  the  various  intellectual  operations  performed  upon 
such  elements. 

The  primary  functions  of  the  intelligence  will  be  classed,  as 
demanded  by  undeniable  facts,  under  a  threefold  division,  to 
wit :  sense,  the  faculty  which  gives  us  the  qualities  of  external 
material  substances  ;  consciousness,  the  faculty  which  perceives 
and  apprehends  the  phenomena  of  the  mind  itself,  or  internal 
phenomena ;  and  reason,  the  faculty  or  function  of  the  intelli- 
gence which  gives  the  logical  antecedents  of  the  phenomena 
given  by  sense  and  consciousness,  that  is,  the  ideas  of  space, 
time,  substance,  cause,  the  finite  and  the  infinite,  of  a  whole  in- 
cluding parts,  of  right  and  wrong,  law,  &c.  The  elements  of 
all  our  knowledge  will  be  shown  to  be  given  by  these  three 
functions  of  the  intelligence.  Having  determined  the  character 
of  these  classes  of  phenomena — their  mutual  relationships  and 
dependencies,  and  consequently  the  relations  of  these  faculties 
to  one  another — the  next  department  of  inquiry  will  be  the 
secondary  faculties  or  functions  of  the  intelligence.  Here,  first 
of  all,  those  intellectual  operations  by  which  the  elements  of 
thought  given  by  the  primary  faculties  are  combined  into  con- 
ceptions or  notions  particular  and  general,  will  claim  special 
attention — the  faculty  by  which  such  operations  are  performed 
being  denominated  the  understanding,  the  conceptive  or  notion- 
forming  power. 

The  faculty  next  considered  will  be  that  in  which  the  various 


relations,  intuitive  and  deductive,  existing  between  conceptions 
or  notions,  are  affirmed,  that  is,  the  faculty  of  judgment. 

Then  the  associative  principle,  including  memory  and  recol- 
lection— the  principle  by  which  former  intellectual  states  are  re- 
vived by  means  of  present  mental  states — will  be  elucidated. 

The  last  object  of  inquiry  will  be  the  imagination,  that  facul- 
ty or  function  of  the  intelligence  by  which  the  elements  of 
thought  given  by  the  other  faculties  are  blended  into  concep- 
tions corresponding,  not  like  conceptions  of  the  understanding 
with  realities  as  they  are,  but  with  fundamental  ideas  in  the 
mind  itself,  ideas  of  the  beautiful,  the  grand,  the  sublime,  &c. 

A  system  of  intellectual  philosophy  thus  developed  undenia- 
bly realizes  the  true  idea  of  science  in  accordance  with  the 
necessary  laws  of  scientific  definition,  logical  division  and  ar- 
rangement of  topics.  It  will  readily  be  seen  that  each  function 
of  the  intelligence  referred  to  really  exists,  and  is  as  really  dis- 
tinct from  every  other,  and  at  the  same  time  that  these  different 
faculties  include  all  conceivable  intellectual  operations.  Every 
intellectual  operation  must  be  an  intuition  of  one  or  the  other 
of  the  primary  faculties — a  notion  or  conception,  that  is,  an 
operation  of  the  understanding — a  judgment  intuitive  or  deduc- 
tive, or  a  phenomenon  of  the  faculty  of  judgment — an  act  of 
memory  or  recollection — or  a  creation  of  the  imagination. 
There  are  just  this  number  of  intellectual  faculties  or  functions, 
and  there  can  be  no  more.  Such  would  be  the  general  charac- 
ter of  a  system  of  intellectual  philosophy  developed  according 
to  the  German,  or  what  we  regard  as  the  only  scientific  method. 

Let  us  now  contemplate  an  example  of  a  system  developed  in 
conformity  to  the  fragmentary  method,  to  which  most  systems 
in  this  department  of  science  developed  by  the  Anglo-Saxon 
mind  conform.  The  following  is  the  fist  and  order  of  topics  in- 
vestigated by  an  author  of  great  merit,  whose  work  appeared  a 
few  yeai*s  since.  After  certain  preliminary  observations,  the 
author  proposes  to  investigate  the  following  subjects :  I.  Per- 
ception ;  in  one  section  under  this  division  the  subject  of  concep- 
tions or  notions  is  considered.     II.  Consciousness.     III.  Origi- 


APPLIED     LOGIC.  303 

nal  suggestion  or  apprehension.     IV.  Abstraction.     V.  Memo- 
ry.   VI.  Reasoning.    VII.  Imagination.     VIII.  Taste. 

This  division  and  arrangement  of  topics  in  general  accords, 
and  in  no  essential  particular  differs,  from  most  of  the  popular 
treatises  on  this  science  now  before  the  English  and  American 
public.  In  regard  to  such  a  method  of  elucidating  this  science, 
we  would  invite  special  attention  to  the  following  suggestions  : 
1.  There  is  here  no  proper  recognition  of  the  fundamental  dis- 
tinction between  the  primary  and  secondary  functions  of  the 
intelligence,  and  no  elucidation  of  their  mutual  relationships 
and  dependencies  upon  one  another.  2.  This  distinction  is 
confounded,  conceptions  or  notions  being  treated  of  prior  to 
two  of  the  primary  faculties,  consciousness  and  oi-iginal  sug- 
gestion. 3.  From  the  form  and  connection  in  which  concep- 
tions are  treated  of,  it  is  implied  that  they  pertain  only  to  ex- 
ternal objects,  while  we  have,  in  fact,  conceptions  respecting 
mind  as  well  as  matter.  4.  More  than  all,  abstraction,  rea- 
soning, and  taste,  are  presented  as  distinct  functions  of  the  gen- 
eral intelligence,  whereas  they  are  all  only  different  functions 
of  a  single  faculty  of  that  intelligence,  to  wit,  the  judgment. 
To  judge  that  different  elements  of  a  given  conception  are  un- 
like to  each  other,  and  thus  to  separate  them  the  one  from  the 
other — that  is,  to  make  abstraction  of  a  given  conception,  to 
judge  in  view  of  the  relations  of  given  conceptions  to  some 
common  one,  that  they  agree  or  disagree  with  one  another — 
that  is,  to  reason,  and  to  affirm  of  certain  objects  or  acts,  that 
one  is  beautiful,  grand,  sublime,  or  the  opposite — that  is,  those 
intellectual  operations  denominated  taste,  do  not  present  the 
operations  of  different  functions  of  the  general  intelligence,  but 
diverse  operations  of  one  and  the  same  faculty  of  that  intelli- 
gence— the  judgment.  5.  We  have  in  all  such  cases,  in  short, 
a  mere  aggregation  of  topics  connected  with  this  science  in  the 
almost  total  absence  of  all  conformity  to  the  laws  and  principles 
-of  logical  division  of  subjects  and  scientific  arrangement  of 
topics.  It  is  needless  to  add,  that  by  means  of  such  a  method 
it  is  impossible  to  attain  to  the  real  science  of  the  human  intel- 


We  have  given  the  above  examples  for  the  express  purpose 
of  impressing  upon  all  the  fundamental  importance  of  scientific 
method  in  the  treatment  of  all  subjects  of  thought. 

The  character  of  any  System  of  Intellectual  Philosophy  which 
shall  meet  the  fundamental  wants  of  this  age. 

Before  dismissing  the  subject  of  intellectual  philosophy  we 
would  direct  special  attention  to  one  inquiry  pertaining  to  this 
subject,  to  wit,  the  character  of  any  system  in  this  department 
of  thought  and  investigation  which  shall  meet  the  fundamental 
wants  of  this  age.  Among  these  characteristics  we  simply  no- 
tice the  two  following : 

1.  The  system  itself  will  be  developed  in  strict  accordance 
with  the  principles  of  scientific  method  above  elucidated.  Any 
system  developed  according  to  the  fragmentary  method  will 
leave  the  great  want  under  consideration  unmet. 

2.  The  system  must  be  so  developed  that  the  principles  eluci- 
dated shall  underlie  and  lead  to  the  distinct  solution  of  those 
great  questions  which  lie  wholly  within  the  sphere  of  intellectual 
science,  and  which  are  now  pressing  everywhere  upon  the  phi- 
losophic mind — questions  pertaining  to  the  distinct  and  oppo- 
site systems  of  realism,  materialism,  and  idealism  in  its  various 
forms.  One  of  these  systems,  to  the  exclusion  of  all  the  others, 
must  be  true,  and  it  belongs  exclusively  to  this  one  science  to 
furnish  the  principles  by  which  the  question  pertaining  to  the 
validity  of  each  may  be  solved.  Any  systems  that  fail  to  furnish 
and  elucidate  such  principles  fail  utterly  to  meet  one  of  the  most 
fundamental  wants  of  the  age,  a  want  which  science  is  bound 
to  meet.  Each  of  the  systems  of  materialism  and  idealism  is 
either  true  or  false,  and  science  is  bound  to  show  which.  The 
influence  of  these  systems  upon  the  public  mind  can  be  de- 
stroyed, not  by  ignoring  the  subject,  nor  by  railing  against  the 
consequences  to  which  any  such  system  leads,  but  by  a  demon- 
stration of  the  invalidity  of  its  claims.  Here,  as  it  appears  to 
us,  lies  the  grand  defect  in  our  systems  of  intellectual  philoso- 
phy as  commonly  taught  in  the  progress  of  a  liberal  education. 


APPLIED     LOGIC.  305 

The  method  pursued  in  such  systems  is  for  the  most  part,  to 
say  the  least,  of  the  fragmentary  instead  of  the  truly  scientific 
character.  Then,  when  the  student  leaves  his  alma  mater, 
with  the  impression  that  he  understands  this  science,  he  finds 
himself  confronted  with  systems  of  intellectual  science  utterly 
subversive  of  all  his  ideas  of  God,  immortality,  and  retribution 
— systems  apparently  possessing  the  highest  perfection  of  scien- 
tific development,  and  commended  to  his  regard  by  the  highest 
forms  of  apparent  philosophic  deduction.  These  systems  pre- 
sent great  problems  which  undeniably  fall  within  the  appro- 
priate and  exclusive  sphere  of  the  science  in  which  he  has  sup- 
posed himself  to  have  been  fully  taught,  and  yet  he  finds  him- 
self furnished  with  no  principles  by  which  he  can  discern  the 
invalidity  of  the  systems  themselves,  or  give  any  other  solutions 
to  these  problems  than  those  furnished  by  said  systems.  Un- 
der such  circumstances,  the  philosophic  mind  is  impressed  with 
the  consciousness  that  it  must  either  ignore  philosophy  itself — 
what  few  such  minds  will  do — or  embrace  some  one  of  the  sys- 
tems referred  to,  or  else  hang  in'  painful  suspense  in  regard  to 
the  question,  What  is  truth  ?  Systems  which  leave  the  great 
problems  of  philosophy  in  such  a  state,  must  be  fundamentally 
unadapted  to  meet  the  pressing  wants  of  the  age. 


EEBOE  OF  ME.  MILL  IN  REGAED  TO  THE  SYLLOGISM. 

"  It  must  be  granted,"  says  Mr.  Mill,  "  that  in  every  syllo- 
gism, considered  as  an  argument  to  prove  the  conclusion,  there 
is  a  petitio  principii.    When  we  say, 

All  men  are  mortal ; 
Socrates  is  a  man  ; 
Therefore,  Socrates  is  mortal ; 

it  is  unanswerably  urged  by  the  adversaries  of  the  syllogistic 
theory  that  the  proposition,  '  Socrates  is  mortal,'  is  presupposed 
in  the  more  general- assumption,  'All  men  are  mortal;'  that  we 
cannot  be  assured  of  the  mortality  of  all  men,  unless  we  are 
previously  certain  of  the  mortality  of  every  individual  man ; 


that  if  it  be  still  doubtful  whether  Socrates,  or  any  other  indi- 
vidual you  choose  to  name,  be  mortal  or  not,  the  same  degree 
of  uncertainty  must  hang  over  the  assertion,  '  All  men  are  mor- 
tal ;'  that  the  general  principle,  instead  of  being  given  as  evi- 
dence of  the  particular  case,  cannot  itself  be  taken  for  true  with- 
out exception,  until  every  shadow  of  doubt  which  could  effect 
any  case  comprised  with  it,  is  dispelled  by  evidence  aliunde  / 
and  then  what  remains  for  the  syllogism  to  prove  ? — that,  in 
short,  no  reasoning  from  generals  to  particulars  can,  as  such, 
prove  any  thing  ;  since  from  a  general  principle  you  cannot  in- 
fer any  particulars,  but  those  which  the  principle  itself  assumes 
as  foreknown." 

In  reply,  we  remark  in  the  first  place,  that  what  Mi\  Mill 
has  here  affirmed  to  be  true  of  the  syllogism  universally,  has  no 
application  whatever  to  any  but  syllogisms  of  a  certain  class, 
and  even  in  respect  to  these  his  assertions  do  not  hold.  In  all 
cases  where  the  major  proposition  represents  a  strictly  necessa- 
ry and  universal  truth  or  principle,  and  the  minor  presents  a 
fact  coming  under  said  principle,  there  is  not  even  the  appear- 
ance of  the  petitio  principii.    For  example : 

Things  equal  to  the  same  things  are  equal  to  one  another ; 

A  and  B  are  each  equal  to  C  ; 

Therefore,  A  and  B  are  equal  to  one  another. 

Where  is  even  the  appearance  of  the  fallacy  under  considera- 
tion in  this  case  ?  and  the  syllogism  of  most  of  the  sciences  is 
exclusively  of  this  character. 

In  cases  where  the  major  premise,  as  in  the  proposition,  "All 
men  are  mortal,"  is  a  general  principle  or  truth  of  induction, 
which  Mr.  Mill  falsely  assumes  to  hold  of  all  scientific  princi- 
ples, he  would  have  us  suppose  that  the  truth  of  said  principle  is 
y*-     .  *  assumed,  that  is,  begged  without  proof.    We  observe  a  certain 

number  of  cases  of  a  certain  class,  and  find  a  certain  fact  to  be 
true  of  them.  From  such  mere  coincidences  we  assume  that 
the  same  fact  is  connected  with  all  the  individuals  of  the  class 
referred  to,  and  then  from  this  mere  assumption  we  reason  back 
to  each  individual  of  said  class.  Now  it  is  not  true  in  fact  that 
general  truths  of  this  character  even  are  affirmed  for  the  reason 


APPLIED     LOGIC.  307 

here  assigned.  Such  deductions,  on  the  other  hand,  rest  upon 
the  principle  stated  by  Kant,  to  wit :  that  where  a  great  multi- 
tude of  facts  of  a  given  species  universally  agree  in  some  one 
particular,  there  is,  in  the  nature  of  the  facts  themselves,  "  some 
common  ground"  for  such  agreement — a  ground  which,  of 
course,  must  hold  true  of  all  facts  of  the  same  species  subse- 
quently met  with.  It  is  in  view  of  this  principle,  that  all  gen- 
eral principles  of  the  character  under  consideration  are  affirmed. 
The  validity  of  the  general  principle  is  not  begged,  as  Mr.  Mill 
affirms,  but  affirmed  in  view  of  a  valid  reason.  It  is  not  neces- 
•  sary  for  us  to  observe  every  solitary  fact  of  a  given  class,  to 
know  the  law  of  their  existence  and  occurrence.  When  a  suf- 
ficient  number' has  been  observed  to  discover  said  law,  we  then 
rank  all  particular  facts  of  this  class  under  that  law.  We  have 
not  seen  each  individual  of  the  race  die.  We  have  seen  a  suffi- 
cient number,  however,  to  perceive  that  mortality  is  not  an  acci- 
dent, but  the  law  of  human  existence  in  its  present  state.  This 
law  is  expressed  in  the  proposition,  "All  men  are  mortal."  In 
no  particular,  therefore,  does  the  principle  of  Mr.  Mill  hold 
true  of  the  syllogism. 


ERROR  OF  ME.  MILL  IN  REGARD  TO  THE  NATURE  OP  ALL 
PORMS  OF  INFERENCE. 

As  the  syllogism  in  all  its  forms  contains,  according  to  Mr. 
Mill,  a  petitio  principii,  he  from  hence  concludes  that  in  no 
instance  do  we  really  reason  or  draw  inferences  from  general 
principles,  but  in  all  instances  that  we  reason  "from  particulars 
to  particulars."  "  All  inference,"  he  says,  "  is  from  particulars 
to  particulars  ;  general  propositions  are  merely  registers  of  such 
inferences  already  made,  and  short  formula  for  making  more. 
The  major  premise  of  a  syllogism  consequently  is  a  formula  of 
this  description  ;  and  the  conclusion  is  not  an  inference  drawn 
from  the  formula,  but  an  inference  drawn  according  to  the 
formula  ;  the  real  logical  antecedent  or  premises  being  the  par- 
ticular facts  from  which  the  general  proposition  was  collected 
by  induction." 


308  LOGIC. 

In  the  above  conclusion,  Mr.  Mill  has  undeniably  been  mis- 
led by  his  very  limited  "  particular  facts."  He  found  that  in 
a  few  cases  of  inductions  of  a  particular  kind,  there  was  an  ap- 
pearance of  inference  "  from  particulars  to  particulars."  This 
mere  appearance  of  inference,  in  accordance  with  his  principle, 
he  "  made  into  a  short  formula  for  making  more,"  that  is,  into 
a  universal  formula  for  the  explanation  of  all  inferences  of 
every  kind.  The  major  premise  or  "real  logical  antecedent," 
in  all  the  leading  sciences,  instead  of  being  "  a  formula  of  this 
description,"  is  an  exclusively  analytical  judgment,  a  universal 
and  necessary  truth  whose  invalidity  is  both  inconceivable  and 
impossible  ;  and  it  is  not  merely  according  to,  but  from,  these 
universal  and  necessary  truths  that  all  the  inferences  in  such 
sciences  are  deduced.  Do  we,  for  example,  believe  the  propo- 
sition, "  Things  equal  to  the  same  things  are  equal  to  one 
another,"  because  we  have  tried  the  experiment  and  found  the 
principle  to  hold  in  certain  particular  cases,  and  because  we 
have  from  hence  made  these  individual  deductions  into  short 
formulas  for  making  more  ?  By  no  means.  This  judgment  is 
exclusively  analytic,  as  we  have  formerly  shown,  and  therefore 
absolutely  universal  and  necessary.  We  have  not  come  to  the 
knowledge  of  it,  as  such,  by  experiment  in  particular  cases,  but 
by  direct  and  immediate  intuition.  The  major  premise,  we  re- 
peat, in  all  the  leading  sciences  is  precisely  such  a  truth,  and 
all  inferences  in  such  sciences  is  from,  and  not  according  to, 
such  truths.  Even  in  those  cases  also  which  apparently  favor 
Mr.  Mill's  theory,  we  do  not  reason  from  individual  facts  to  in- 
dividual facts,  but  from  certain  facts  of  a  given  class  to  the  law 
which  governs  said  facts,  and  then  from  this  law  to  all  the  facts 
of  said  class.  There  never  was  an  inference  more  wide  from 
the  truth,  and  less  authorized  by  the  facts  from  which  it  is  de- 
duced, than  that  of  Mr.  Mill  in  regard  to  the  syllogism,  on  the 
one  hand,  and  all  forms  of  inference,  on  the  other. 


APPLIED     LOGIC.  309 

ME.    MILL'S   POSITION   THAT    "THE   SYLLOGISM   IS   NOT   THE   TYPE 
OF   REASONING,    BUT   A   TEST    OF    IT." 

Mr.  Mill,  in  accordance  with  the  principles  of  his  theory, 
affirms  that  "  the  syllogism  is  not  a  correct  analysis  of  reason- 
ing or  inference."  Yet  he  goes  on  to  show,  that  if  we  wish  to 
test  the  validity  of  a  reasoning  process  we  must  make  use  of  the 
syllogism  to  do  it.  "  It  is  not  the  form,"  he  tells  us,  "  in  which 
we  must  reason,  but  it  is  a  form  in  which  we  may  reason,  and 
into  which  it  is  indispensable  to  throw  our  reasoning  when  there 
is  any  doubt  of  its  validity."  The  syllogism,  he  asserts,  always 
involves  a  logical  error,  a  petitio  principii,  and  "  is  not  a  cor- 
rect analysis  "of  reasoning  or  inference,"  and  that  it  is  only  when 
"  there  is  no  suspicion  of  error  that  we  are  permitted  to  use  the 
true  process,"  that  is,  reason  -from  particulars  to  particulars, 
"from  the  known  particular  cases  to  unknown  ones."  Now 
here  are  a  greater  number  of  palpable  contradictions  than  we 
have  space  to  notice.  We  will,  therefore,  specify  only  two  or 
three  of  them.  The  petitio  principii — begging  the  question — 
is,  according  to  all  the  rules  of  logic,  one  of  the  most  vicious 
forms  of  reasoning,  a  form,  therefore,  never  to  be  employed ; 
and  the  syllogism,  according  to  Mr.  Mill,  in  all  its  forms,  in- 
volves this  very  fallacy.  Yet,  according  to  him  the  following 
facts  are  true  of  the  syllogism  :  1.  In  no  case  is  it  "a  form  in 
which  we  must  reason ;"  but  it  is  only  "  when  the  case  is  familiar 
and  little  complicated,  and  there  is  no  suspicion  of  error,"  that 
we  may  use  that  form  which  he  affirms  to  be  the  only  correct 
"  analysis  of  the  reasoning  process,"  the  form  in  which  in  reali- 
ty we  always  do  reason,  that  is,  "  reason  at  once"  from  particu- 
lars to  particulars,  "  from  known  particular  cases  to  unknown 
ones."  Now  if  in  all  cases  but  the  one  here  specified,  we  may 
not  reason  according  to  Mr.  Mill's  formula,  that  is,  from  par- 
ticulars to  particulars,  and  in  no  case  are  we  obliged  to  use  the 
syllogistic  form,  there  must  remain  a  third  form  which  is  valid 
universally,  or  Mr.  Mill  has  most  palpably  contradicted  him- 
self. But  no  third  form  exists,  and  Mr.  Mill  has  contradicted 
himself.     2.  According  to  Mr.  Mill's  express  teachings,  a  form 


y^m^ 


of  reasoning  always  vicious,  and  according  to  the  immutable 
laws  of  reasoning  never  to  be  employed,  always  may  be  em- 
ployed. 3.  Into  this  most  vicious  and  never  to  be  used  form, 
"  it  is  indispensable  to  throw  our  reasoning  when  there  is  any 
doubt  of  its  validity."  4.  The  syllogism  which  presents  a  false 
analysis  of  the  reasoning  process,  and  in  all  its  forms  involves 
one  of  the  most  vicious  forms  of  fallacy,  is,  after  all,  the  only 
proper  test  of  the  validity  of  any  reasoning  process  whatever. 
This  is  sufficient  to  demonstrate  one  fact,  to  wit,  that  Mr.  Mill 
must  have  fundamentally  misapprehended  the  nature  of  the 
reasoning  process  in  all  its  forms. 

Exclusive  condition  on  which  we  can  legitimately  reason  from 
particulars  to  particulars. 

Before  dismissing  this  subject,  attention  should  be  directed  to 
one  important  inquiry — the  exclusive  conditions  on  which  we 
can  in  any  form  legitimately  reason  from  particulars  to  particu- 
lars, that  is,  from  one  individual  to  another.  Two  individuals 
are  before  us — A  and  B.  We  have  immediate  knowledge  of 
the  fact,  that  a  certain  element  C  exists  in  A,  and  have  no  such 
knowledge  relatively  to  B.  On  what  condition  can  we  infer 
that  because  A  has  C,  B  has  it  also  ?  On  this  condition  only, 
that  A  and  B  have  in  common  another  element  M,  and  that  M 
and  C  are  necessarily  connected,  so  that  where  M  is,  C  is  also. 
Then,  and  then  only,  can  we  affirm  positively  that  because  A 
has  C,  B  has  it  also.  If  the  connection  between  M  and  C  is 
merely  accidental,  we  cannot  reason  at  all  from  A  to  B.  If  we 
do  not  know  whether  this  connection  is  necessary  or  accidental, 
then  our  reasoning  is,  as  Mr.  Mill  himself  has  shown,  analogi- 
cal and  not  inductive.  We  never,  then,  in  accordance  with  the 
formula  of  Mr.  Mill,  reason  from  particulars  to  particulars,  and 
this  Mr.  Mill  himself  has  fully  shown  in  other  parts  of  his  work. 
On  the  other  hand,  our  reasoning  from  individuals  to  indi- 
viduals is  always  in  view  of  some  element  common  to  the  two, 
together  with  the  known  relations  of  this  common  element  to 
another  known  to  exist  in  one  individual,  and  not  otherwise 


APPLIED     LOGIC.  311 

than  inferentially  known  to  exist  in  the  other.     In  such  cases 
our  reasoning  is  always  from  a  general  truth,  to  wit,  Every  in- 

lividual  which  has  the  common  element  M  has  the  implied 

>ne  C. 


RELATIONS    OF   THE   SYLLOGISM   TO   THE   DISCOVERY    OF   TRUTH. 

It  is  a  doctrine  of  Mr.  Mill  and  other  logicians,  that  in  no 
case  do  we,  hy  means  of  the  syllogism,  discover  truth,  its  only 
use  being  the  proof  of  truth  when  discovered.  By  investiga- 
tion we  discover,  and  by  the  syllogism  we  prove  what  has  been 
discovered.  To  this  dogma  we  by  no  means  yield  our  assent. 
On  the  other  hand,  we  believe  that  all  inferred  truth  is  origi- 
nally discovered,  as  well  as  subsequently  proved,  by  means  of 
the  syllogism,  and  can  be  discovered  by  no  other  means.  An 
individual,  for  example,  may  know  perfectly  the  relations  of 
two  objects  A  and  B  to  a  common  third  C.  Yet  he  may  never 
have  perceived  the  inference  involved  in  these  relations.  The 
individual  who  points  out  that  inference  as  really  conveys  a  new 
truth  to  that  person,  as  the  one  who  conveyed  to  him  a  know- 
ledge of  the  relations  referred  to.  Yet  this  new  truth  is  re- 
vealed wholly  by  means  of  the  syllogism.  A  jury  may  have 
before  them  all  the  facts  bearing  upon  a  given  case,  and  yet  not 
perceive  at  all  the  real  bearing  of  these  facts  upon  that  case. 
The  advocate  or  judge  who  reveals  to  them  the  conclusions  in- 
volved in  said  facts,  as  really  makes  a  discovery  to  them  as  the 
witnesses  who  revealed  to  them  the  facts.  Yet  those  conclu- 
sions were  wholly  revealed  by  means  of  the  syllogism.  Every 
inference  when  first  obtained  is  a  newly  discovered  truth,  a 
truth  discovered  by  means  of  the  same  premises  by  which  it  is 
subsequently  proven.  These  remarks  apply  to  inferred  truth 
in  all  its  forms.  This  is  first  discovered  and  then  subsequently 
proven  by  the  same  means,  the  syllogism.  Investigation  conse- 
quently has  two  directions — facts  for  the  purpose  of  discovering 
premises,  and  premises  for  the  purpose  of  discovering  the  de- 
ductions or  inferences  which  they  yield.  The  inference,  as 
originally  given,  is  as  much  a  discovery  as  the  facts,  and  the 


312  LOGIC. 

inference,  we  repeat,  is  always  obtained  by  means  of  the  syllo- 
gism. 

\/  THE  GREAT  PROBLEM   IN   PHILOSOPHY   ACCORDING  TO   KANT. 

In  his  "  Critick  of  Pure  Reason,"  Kant  has  rendered  demon- 
strably evident  the  actual  existence  in  the  human  intelligence  of 
"  cognitions  d  priori'''' — that  is,  of  ideas  and  principles  having  the 
characteristics  of  absolute  universality  and  necessity  ;  such,  for 
example,  as  the  principle,  "  Body  supposes  space," — "  Succession, 
time," — "  An  event  a  cause,"  &c.  In  demonstrating  the  reality 
of  such  principles  he  has  rendered  equally  evident  the  fact,  that 
the  fundamental  principle  of  the  philosophy  of  Locke,  that  all 
our  knowledge  is  derived  from  experience,  is  and  must  be  false. 
No  man  can,  by  any  possibility,  read  and  understand  the  first 
five  or  six  pages  of  the  "  Critick,"  and  remain  a  disciple  of  the 
empirical  philosophy.  By  experience  we  only  learn,  and  can 
only  learn,  what  is  true  in  a  certain  number  of  particular  cases, 
but  never  what  is  and  must  be  true  in  all  cases  universally. 
As  a  matter  of  fact,  we  have  cognitions  of  which  we  know  ab- 
solutely, that  they  not  only  are  true  in  certain  cases,  but  that 
they  are  and  must  be  true  in  all  cases.  Such  cognitions,  there- 
fore, never  could  have  been  derived  from  experience.  All  such 
cognitions  Kant  denominates  "  synthetic  cognitions  d  priorV 
Having  demonstrated  the  existence  of  such  cognitions,  he  pro- 
poses this  one  question  as  the  then  great  problem  in  philosophy, 
to  wit :  "  How  are  synthetic  cognitions  d  priori  possible  ?" 
"  All  metaphysicians  consequently,"  he  says,  "  are  solemnly  and 
legally  suspended  from  their  occupations,  till  they  shall  have 
answered  in  a  satisfactory  manner  the  question,  How  are  syn- 
thetic judgments,  d priori,  possible?"  In  this  statement  Kant 
was  unquestionably  right,  and  philosophy  can  never  be  placed 
permanently  on  the  track  of  truth,  till  this  question  is  correctly 
/     answered. 


APPLIED     LOGIC.  313 

KanVs  solution  of  this  Problem. 

The  following  is  Kant's  solution  of  this  problem.  Through 
the  action  of  some  unknown  and  unknowable  cause,  a  certain 
feeling — sensation — is  produced  in  the  mind.  On  occasion  of 
such  feeling  being  excited,  the  ideas  of  time  and  space,  by  the 
spontaneous  action  of  the  intelligence,  are  awakened  in  the 
mind.  Through  these  ideas  the  sensation  which  is  purely  and 
exclusively  a  subjective  state,  appears  to  the  mind  as  an  object 
external  to  the  mind,  an  object  having  extension,  form,  color, 
&c.  We  do  not  first  perceive  an  external  object,  and  then,  as 
the  ideas  of  time  and  space  are  thus  awakened  in  the  mind, 
conceive  of  it  as  existing  in  time  and  space.  On  the  other 
hand,  these  ideas  are  originated  independently  of  perception 
and  prior  to  it,  and  when  awakened  cause  the  sensation  to  ap- 
pear as  an  object  external  to  the  mind.  The  sensation,  he  af- 
firms, is  the  content  of  the  perception,  the  only  thing  really  per- 
ceived, while  the  ideas  under  consideration  give  "the  form 
thereof,"  that  is,  make  the  sensation  appear  as  an  external  ob- 
ject having  extension  and  form.  Under  the  influence  of  other 
d  priori  ideas  subsequently  awakened  in  a  similar  manner  to 
the  former  ones,  the  object  thus  perceived  is  conceived  of  as  a 
substance  having  qualities,  as  acting  upon  other  substances,  and 
being  acted  upon  by  them,  as  existing  in  time  and  space,  &c. 
Thus  it  is  that  the  universe,  with  God  as  its  author,  rises  before 
the  mind.  The  universe  which  we  seem  to  see,  and  conceive  of 
as  a  great  reality  really  and  truly  external  to  the  mind,  has  no 
real  existence  out  of  the  mind  itself.  The  universe  which  we 
actually  perceive  is  nothing  but  sensation  made  to  appear 
through  d  priori  ideas,  as  a  universe  external  to  the  mind ; 
and  God  is  nothing  but  an  ideal  cause  of  an  ideal  creation. 
On  no  other  supposition,  he  affirms,  can  we  account  for  the  ex- 
istence of  d  priori  cognitions,  and  sciences  such  as  the  pure 
mathematics,  in  the  mind.  A  priori  ideas,  he  assumes,  must 
be  derived  from  experience,  that  is,  be  directly  and  immediate- 
ly given  by  perception  external  and  internal,  or  they  must  exist 
in  the  mind  prior  to  perception  and  independent  of  it,  and  them- 


selves  determine  the  perception  and  all  subsequent  mental  oper- 
ations. The  first  hypothesis  is  not,  and  cannot  he,  true.  The 
second,  therefore,  must  be  true.  The  universe,  then,  which  we 
perceive,  is  not  an  object  external  to  the  mind,  an  object  which 
the  intelligence  as  a  power  of  knowledge  perceives  as  it  is,  but  a 
mere  succession  of  sensations  which,  through  these  d  priori 
ideas,  are  made  to  appear  as  such  a  universe.  The  universe  is 
not  to  the  mind  an  object,  and  the  mind  to  it  a  faculty  of  know- 
ledge ;  and  knowledge  does  not  exist  in  consequence  of  this  cor- 
relation between  the  two.  The  external  universe,  on  the  other 
hand,  is  nothing,  we  repeat,  but  sensation  itself,  made  to  appear 
as  such  by  means  of  d  priori  ideas  awakened  in  the  mind  on 
occasion  of  sensation  by  the  spontaneous  activity  of  the  intelli- 
gence itself.  If  these  ideas  are  awakened  prior  to  all  other 
intellectual  operations,  prior  to  all  perception  external  or  in- 
ternal, if  they  give  form  and  direction  to  perception  and  all 
other  intellectual  operations,  then  we  can  see  clearly  how  we 
can  have  from  these  ideas  pure  d  priori  sciences,  such  as  the 
pure  mathematics — sciences,  all  of  whose  principles  and  deduc- 
tions shall  have  the  same  characteristics  of  universality  and  ne- 
cessity which  their  original  principles  have.  We  can  see,  too, 
how  it  is  that  all  the  facts  of  the  universe  shall  accord  with 
these  d  priori  ideas  and  principles.  Inasmuch  as  the  latter  de- 
termine the  former  universally,  there  must  be  this  accordance 
between  them.  On  no  other  supposition,  Kant  affirms,  can  the 
existence  of  the  pure  sciences  be  accounted  for,  together  with 
the  perfect  and  universal  accordance  of  all  the  facts  of  the  uni- 
verse with  the  principles  and  deductions  of  these  sciences. 
Such  is  Kant's  solution  of  the  great  problem  in  philosophy 
which  he  has  himself  propounded.  Let  us  now  contemplate 
the  fundamental  mistakes  into  which  he  has  fallen  in  the  solu- 
tion of  that  problem.    Among  these  we  notice  the  following : 

Errors  of  Kant  in  the  solution  of  this  Problem. 

1.  The  first  error  that  we  notice  is  found  in  the  assumption 
which  lies  at  the  basis  of  this  solution.    The  assumption  is  this : 


APPLIED     LOGIC.  315 

Either  d  priori  ideas  and  principles  are  given  directly  and  im- 
mediately by  experience  (perception  external  and  internal),  ac- 
cordi«g  to  the  theory  of  Locke,  or  they  must  arise  in  the  mind 
by  the  spontaneous  action  of  the  intelligence,  and  that  inde- 
pendent of  and  prior  to  all  acts  of  perception,  external  or  inter- 
nal, according  to  the  theory  of  Kant.  One  of  these  theories, 
he  assumed,  must  be  true,  because  none  other  is  conceivable  or 
possible.  The  former  cannot  be  true.  The  latter,  consequent- 
ly, must  be  true. 

The  error  of  Kant  in  the  above  assumption  is  obvious  and 
undeniable.  He  assumes  that  one  or  the  other  of  these  theo- 
ries must  be  true,  because  none  other  is  conceivable  or  possible. 
Now  there  is  a  third  theory — differing  alike  from  that  of  Locke, 
on  the  one  hand,  and  that  of  Kant,  on  the  other — a  theory  which, 
in  common  with  the  latter,  recognizes  the  reality  of  all  d  priori 
cognitions,  and  as  fully  and  perfectly  as. that  accounts  for  the 
same,  together  with  all  other  forms  of  knowledge.  Let  us  sup- 
pose that  the  universe  exists  as  relatively  to  mind  an  object, 
and  mind  to  exist  as  relatively  to  the  universe  a  power  or 
faculty  of  knowledge.  Let  us  suppose  further,  that  while  there 
is  in  the  intelligence  a  power  to  perceive  existing  substances  as 
they  are,  there  is  also  in  the  same  intelligence  the  power  to  ap- 
prehend other  realities  necessarily  supposed  by  those  which  are 
the  objects  of  perception.  In  other  words,  let  us  suppose  that 
the  intelligence  not  only  has  the  power  to  perceive  body,  for 
example,  but  on  occasion  of  such  perception,  to  apprehend  the 
reality  of  space,  which  must  exist  or  body  cannot  exist.  In 
this  case,  we  should  have  the  idea  of  space  just  as  it  is  given  in 
the  theory  of  Kant.  The  same  power  which,  on  the  perception 
of  extension,  gives  the  idea  of  space,  would,  on  the  perception 
of  succession,  phenomena,  and  events,  give  us  the  ideas  of  time, 
substance,  and  cause.  In  a  similar  manner  the  existence  of  all 
d  priori  ideas  of  every  kind  may  be  accounted  for  : 

With  equal  readiness  can  we  account,  in  consistency  with 
the  principles  of  this  theory,  for  all  d  priori  judgments — the  d 
priori  synthetical  cognitions  of  Kant — with  all  their  character- 
istics.    When  we  reflect  upon  the  relations  of  what  we  perceive 


316  LOGIC. 

to  that  which  we  apprehend  as  necessarily  supposed  as  ante- 
cedently true — that  is,  supposed  by  what  we  perceive — we  see 
at  once,  that  those  relations  are  absolutely  universal  and  neces- 
sary. These  necessary  and  universal  relations  are  expressed  in 
the  principles,  "  Body  supposes  space," — "  Succession,  time," — 
"  Phenomena,  substance," — "  Events  a  cause,"  &c.  When  the 
necessary  or  d  priori  elements  of  thought  are  separated  from 
the  empirical,  and  the  principles  and  logical  consequences  of  the 
same  are  developed,  we  have  the  pure  sciences-1— such  as  the 
mathematics.  When  the  two  forms  of  thought  are  developed 
together,  then  we  have  the  various  mixed  sciences.  Thus  wc 
have  a  theory  of  knowledge  which  gives  us  all  forms  of  know- 
ledge as  they  are,  and  accounts  for  such  knowledge  as  fully  and 
perfectly  as  the  theory  of  Kant.  The  argument  of  Kant,  then, 
for  the  truth  of  his  theory  involves  a  fundamental  fallacy — a  fal- 
lacy in  the  employment  of  the  disjunctive  syllogism.  This  syl- 
logism is  this  :  Either  the  theory  of  Locke  or  my  own  must  be 
true.  The  former  is  not,  and  the  latter  consequently  must  be 
true.  The  true  syllogism  applicable  to  the  case  as  thus  far  pre- 
sented is  this  :  Either  the  theory  of  Locke,  or  one  or  the  other 
of  the  two  under  consideration,  must  be  true.  That  of  Locke  is 
not,  and  therefore  one  of  these — and  so  far  it  does  not  appear 
which — must  be  true.  This  last  syllogism  is  and  must  be  valid, 
for  the  reason  that  there  are  no  other  conceivable  theories  for 
accounting  for  the  existence  of  d  priori  cognitions  in  the  intelli- 
gence but  these  three.  The  whole  transcendental  philosophy, 
therefore — for  all  its  forms  rest  upon  this  one  common  founda- 
tion— rests  exclusively  upon  an  illogical  basis. 

2.  But  we  remark,  in  the  next  place,  that  the  theory  of  Kant 
is  not,  while  the  opposite  theory  is,  in  fact,  true.  According 
to  the  former  theory,  d  priori  ideas — those  of  space  and  time, 
for  example — arise  in  the  mind  prior  to  all  forms  of  perception, 
and,  as  laws  of  thought,  give  form  to  perception  and  all  subse- 
quent intellectual  operations.  Now  we  have  no  consciousness 
whatever  of  any  such  relation  as  this  between  these  ideas  and 
the  act  of  perception.  Who,  by  a  reference  to  consciousness, 
could  perceive  the  truth  of  the  statement  of  Kant,  that  "  space 


APPLIED     LOGIC.  317 

and  time  are  the  pure  forms  of  them"  (perceptions),  that  is, 
make  the  object  perceived  appear  to  the  mind  as  possessed  of 
such  qualities  as  extension  and  shape,  "  sensation  the  matter" — 
that  is,  that  the  thing  really  perceived  is  not  an  object  really 
external  to  the  mind,  but  a  sensation  made  through  the  means 
of  the  ideas  of  time  and  space  to  appear  as  such  object  ?  If 
these  ideas  do  thus  cause  a  purely  and  exclusively  mental  state 
(sensation) — a  state  having  no  extension  or  form — to  appear  to 
the  mind  as  an  external  object  having  extension  and  form,  we 
certainly  have  and  can  have  no  consciousness  of  the  fact.  On 
the  other  hand,  the  testimony  of  consciousness  is  very  distinct  and 
explicit  against  the  theory  of  Kant,  and  in  favor  of  the  one  which 
we  maintain.  We  are  conscious  of  a  direct  and  immediate  per- 
ception of  an  object  external  to  the  mind,  and  then  subsequent- 
ly of  conceiving  of  that  object  as  existing  in  time  and  space. 
According  to  the  distinct  and  explicit  testimony  of  conscious- 
ness, therefore,  the  ideas  of  time  and  space  do  not  arise  in  the 
mind  prior  to  perception  and  as  determining  laws  of  the  same, 
but  subsequently  to  perception  and  as  laws  of  the  secondary 
operations  of  the  intelligence — to  wit,  conceptions  or  notions. 
The  theory  of  Kant  is  undeniably  based  upon  a  manifest  psy- 
chological error.  Ideas  which  exist  in  the  mind  subsequent  to 
perception  and  exclusively  as  laws  of  the  secondary  operations 
of  the  intelligence,  are  given  as  existing  prior  to  perception  and 
as  laws  of  perception  itself— that  is,  of  the  primary  operations  of 
the  intelligence.  A  greater  psychological  error  can  hardly  be 
conceived  of  than  this.  There  is  another  consideration  of  the 
greatest  weight  which  renders  demonstrably  evident  the  fact, 
that  Kant's  theory  of  the  origin  of  d  priori  ideas  and  principles 
is  not,  and  that  that  of  the  opposite  theory  is,  the  true  one.  If 
d  priori  ideas,  those  of  space  and  time,  for  example,  do  arise  in 
the  mind  prior  to  perception,  and  consequently  independently 
of  it,  then  the  objects  of  these  ideas,  time  and  space  themselves, 
may  be  conceived  of  and  defined  by  themselves,  and  without 
any  reference  to  any  of  the  objects  of  perception.  So  of  all 
other  d  priori  ideas.  If  this  were  so,  we  should  also  be  equally 
unable  to  conceive  of  or  define  objects  of  perception  without 


318  LOGIC. 

reference  to  the  objects  of  d  priori  ideas.  Now  the  reverse  of 
all  this  is  undeniably  true  of  both  classes  of  ideas  under  consid- 
eration. We  conceive  of  and  define  no  d  priori  idea  but  by 
referring  to  objects  of  perception,  while  we  can  conceive  of  and 
define  the  latter  class  of  objects  without  referring  to  the  former. 
We  can  conceive  of  and  define  space  and  time,  for  example, 
only  as  the  places  of  bodies  and  events,  and  a  cause  only  as  that 
which  produces  events.  So  of  all  other  d  priori  ideas  of  every 
kind.  Their  objects  can  be  conceived  of  and  defined  but  with 
fixed  reference  to  objects  of  perception.  On  the  other  hand, 
objects  of  perception,  body,  for  example,  may  be  conceived  of 
and  defined,  and  commonly  are  defined,  without  reference  to 
space,  or  other  objects  of  d  priori  ideas.  Such  facts  render  it 
demonstrably  evident  that  d  priori  ideas  do  not,  as  Kant's 
theory  affirms,  arise  in  the  mind  prior  to  perception,  but  that, 
in  accordance  with  the  opposite  theory,  conceptions  of  the  ob- 
jects of  perception  are,  in  all  instances,  the  chronological  ante- 
cedents of  d  priori  ideas.  The  position  of  Cousin  in  regard  to 
the  relation  of  these  two  classes  of  ideas,  the  latter  of  which  he 
denominates,  and  rightly  too,  necessary,  and  the  former  con- 
tingent ideas,  will  unquestionably  stand  the  test  of  time  and  of 
the  most  rigid  psychological  investigation,  to  wit :  that  contin- 
gent ideas  (conceptions  of  objects  of  perception  external  and  in- 
ternal) are  the  chronological  antecedents  of  necessary  ideas, 
— that  is,  the  former  arise  in  the  mind  prior  to  the  latter ;  while 
necessary  ideas  are  the  logical  antecedents  of  contingent  ones, 
— that  is,  we  must  admit  the  reality  of  the  objects  of  the  former 
class  of  ideas,  as  the  condition  of  the  reality  of  the  objects  of  the 
latter  class.  These  undeniable  facts  are  perfectly  fatal  to  the 
claims  of  the  theory  of  Kant  and  of  every  other  form  of  idealism, 
and  as  necessarily  and  absolutely  affirm  the  truth  of  the  oppo- 
site theory,  the  theory  which  we  have  expounded. 

3.  The  theory  of  Kant,  we  remark  finally,  cannot  possibly  be 
true,  because  it  involves  the  greatest  conceivable  contradictions 
and  absurdities.  According  to  this  theory,  when  we  suppose 
ourselves  to  perceive  an  external  object,  the  only  thing  really 
perceived  by  the  mind  is  one  of  its  own  states — a  sensation. 


>  APPLIED     LOGIC.  319 

The  thing  perceived — the  sensation — has  undeniably  neithei 
extension  nor  form.  Yet  it  appears  to  have  both.  It  is  exclu- 
sively a  mental  state.  Yet  it  appears  with  equal  exclusiveness 
as  an  object  external  to  the  mind,  and  having  an  existence  in 
dependent  of  it.  What  is  it  that  imparts  to  such  an  object  such 
an  appearance  ?  The  ideas  of  time  and  space,  says  Kant.  Such, 
also,  is  the  answer  of  idealism  in  all  its  forms.  These  ideas 
(those  of  time  and  space),  it  should  be  bome  in  mind,  pertain 
to  their  objects  as  absolutely  infinite.  Now  here  the  following 
important  questions  arise,  and  demand  distinct  and  specific  an- 
swers from  philosophy:  (1.)  How  can  one  purely  mental  state 
— ideas  pertaining  to  their  objects  as  infinite — cause  another 
purely  and  exclusively  mental  state — a  sensation — to  appear  to 
the  mind  as  an  object  wholly  external  to  the  mind,  and  having 
an  existence  as  wholly  independent  of  it  ?  Idealism  has  never 
answered  this  question,  and  we  are  quite  sure  it  never  will. 
(2.)  How  can  ideas  pertaining  to  their  objects  as  having  infinite 
extension,  give  to  purely  mental  states,  void  wholly  of  all  exten- 
sion, the  appearance  of  having  any  kind  of  extension  whatever  ? 
Is  there  here  even  a  conceivable  relation  of  cause  and  effect  ? 
(3.)  How  can  ideas  which  peitain  to  their  objects  as  having  in- 
finite extension,  cause  mental  states,  void  in  themselves  of  all 
extension,  to  appear  as  possessed  not  only  of  an  external  exist- 
ence, but  finite  extension  ?  Would  not  such  ideas,  if  they  im- 
parted to  such  objects  the  appearance  of  any  extension  at  all, 
impart  that  of  infinite  extension  ?  Is  not  the  opposite  supposi- 
tion a  palpable  absurdity  and  contradiction?  (4.)  How,  we 
ask  finally,  can  ideas  pertaining  to  their  objects  as  exclusively 
infinite,  impart  to  two  sensations,  each  of  which  is  alike  void  of 
all  extension  and  form,  and  therefore  in  these  respects  absolute- 
ly equal,  the  appearance  even  of  not  only  having  definite  ex- 
tension and  form,  but  the  one  as  being  twice  or  a  million  of 
times  as  large  as  the  other  ?  Is  not  here  an  undeniable  viola- 
tion of  the  principle,  "  If  equals  be  added  to  equals,  the  sums 
are  equal  ?"  He  who  assigns  a  cause  for  a  given  effect,  must 
assign  an  intelligibly  adequate  cause,  a  cause,  too,  intelligibly 
adapted  to  produce  the  effect.    The  cause  assigned  by  idealism 


for  external  perception  is  not  only  void  utterly  of  both  these 
characteristics,  but  involves  the  greatest  conceivable  absurdity 
and  self-contradiction.  That  theory,  therefore,  cannot  be  true, 
and  the  opposite  one  must  be  true. 

The  Sensational  Theory  of  External  Perception. 

While  systems  of  intellectual  philosophy  developed  by  the 
Anglo-Saxon  mind  have  generally  repudiated  the  claims  of 
idealism  in  all  its  forms,  they  have,  with  hardly  an  exception, 
admitted  and  affirmed  the  validity  of  that  assumption  upon 
which  every  form  of  that  system  is  based,  to  wit :  that  all  our 
knowledge  of  the  external  universe  is  not  immediate,  but  me- 
diate, and  derived  exclusively  through  the  medium  of  sensation. 
We  are  now  prepared  to  form  a  correct  estimate  of  this  theory 
of  perception.  According  to  its  fundamental  assumption,  what 
we  really  perceive,  when  we  conceive  of  ourselves  as  having  a 
,  perception  of  an  object  external  to  the  mind,  is  not  such  object 
at  all,  but  an  exclusively  mental  state,  a  sensation.  This  pure- 
ly mental  state,  which  is  in  itself  utterly  void  of  all  extension 
and  form,  is,  by  means  of  laws  inhering  in  the  intelligence  itself, 
made  to  appear  as  an  object  wholly  external  and  foreign  to  the 
mind,  an  object  having  extension  and  form.  Against  such  a 
theory  we  urge  the  following  fundamental  objections  : 

1.  The  theory  rests  exclusively  upon  a  mere  assumption,  an 
assumption  for  the  validity  of  which  no  form  or  degree  of  evi- 
dence whatever  can  be  adduced.  No  self-evident  principle  or 
valid  deductions  of  science  can  be  presented  from  which  the  va- 
lidity of  this  theory  can  be  deduced.  This  is  undeniable.  Let 
any  one  attempt  to  prove  the  dogma  that  what  we  really  per- 
ceive, when  we  suppose  ourselves  to  be  actually  perceiving  an 
external  object,  is  no  such  object,  but  a  mere  sensation,  an  ex- 
clusively mental  state,  and  he  will  find  that  he  has  attempted 
an  impossibility. 

2.  This  theory  in  all  its  developments  is  opposed  to  the  direct 
and  absolute  testimony  of  consciousness.  In  the  consciousness 
of  perception  two  factors  are  given  with  equal  absoluteness,  self 


APPLIED     LOGIC.  321 

as  the  subject  of  the  perception,  and  a  not-self  as  its  object.  On 
no  subject  is  the  testimony  of  consciousness  more  distinct  and 
absolute.  In  this  theory,  this  distinction  between  the  self  and 
the  not-self  is  utterly  confounded,  and  each  is  given  as  identical 
with  the  other.  "  Consciousness,  then,"  in  the  language  of  Sir 
William  Hamilton,  "  is  a  liar  from  the  beginning,"  or  this  theo- 
ry is  and  must  be  false. 

3.  This  theory  necessarily  subverts  the  foundation  of  all  valid 
knowledge  of  every  kind.  If  the  intelligence,  by  virtue  of  its 
own  fundamental  and  immutable  laws,  deceives  us,  as  this  theo- 
ry affirms  that  it  does,  in  a  matter  so  fundamental  as  percep- 
tion, then  undeniably  it  is  to  be  trusted  nowhere,  and  know- 
ledge on  any  subject  is  an  absolute  impossibility.  There  is  no 
escaping  this  conclusion.  And  here  permit  us  to  remark,  that 
nothing  conceivable  is  more  unreasonable  than  the  complaints 
of  the  advocates  of  theism  against  the  deductions  of  idealism, 
while  they  themselves  admit  and  affirm  the  foundation-principle 
from  which,  by  an  absolute  necessity,  such  deductions  arise. 
There  is  not  a  deduction  of  idealism  which  cannot  be  shown  to 
have  a  necessaiy  logical  connection  with  this  one  assumption. 

4.  This  theory,  we  remark  finally,  involves  the  most  palpable 
conceivable  absurdities  and  contradictions.  This  we  have  al- 
ready shown  in  our  remarks  upon  the  Kantian  theory  of  per- 
ception. No  philosopher  has  yet  answered,  in  consistency  with 
this  theory,  the  questions :  How  can  a  purely  and  exclusively 
mental  state  be  given  in  consciousness  as  an  object  wholly  ex- 
ternal and  foreign  to  the  mind  ?  How  can  such  a  state,  which 
undeniably  has  neither  extension  nor  form,  be  given  in  con- 
sciousness, not  only  as  an  object  wholly  external  to  the  mind, 
but  also  as  having  both  these  qualities  ?  The  only  answer  ever 
attempted  to  be  given  to  these  questions  is  the  one  already  no- 
ticed, to  wit :  that  this  is  done  through  the  ideas  of  time  and 
space, — a  solution,  as  we  have  shown,  self-contradictory  and  ab- 
surd. As  no  other  solution  is  even  conceivable,  the  theory 
itself  must  be  held  as  utterly  foundationless  and  false.  Yet 
this  theory,  so  utterly  void  of  all  valid  claims  and  so  demon- 
strably false,  has  for  ages  lain  at  the  basis  of  great  systems  of 

14«  , 


theology  and  philosophy.  In  this  connection,  we  are  surely 
strongly  admonished  to  examine  with  great  care  the  principles 
or  first  truths  which  we  lay  at  the  foundation  of  our  systems  of 
belief,  before  we  proceed  to  construct  our  systems  upon  such 
principles. 

THE    GREAT   PROBLEM    IN   PHILOSOPHY    OP   THE   PRESENT   AGE. 

The  progress  of  thought  in  every  age  throws  upon  the  sur- 
face of  the  public  mind  certain  great  problems  in  philosophy, 
problems  which  demand  of  philosophy  a  satisfactory  scientific 
solution.  The  demonstration  of  the  reality  of  d  priori  cogni- 
tions in  the  human  intelligence,  presented  for  solution  the  great 
problem  propounded  by  Kant,  to  wit,  "How  are  synthetic 
cognitions  d priori  possible?"  That  problem,  as  we  judge,  has 
now  received  the  required  solution. 

Were  we  called  upon  to  express  an  opinion  in  regard  to  the 
question,  What  is  the  great  problem  in  philosophy  of  the  present 
age  ?  it  would  be  this  :  By  what  formula  shall  we  represent  this 
one  fundamental  idea,  to  wit,  the  extent,  limits,  and  test  of 
valid  knowledge  ?  Every  system  of  belief,  whatever  its  na- 
ture and  character,  assumes  and  affirms  the  fact  that  there  is : 
1.  Such  a  thing  as  truth  ;  2.  Such  a  thing  as  valid  knowledge 
of  truth ;  and,  3.  Such  a  thing  as  a  valid  test  of  such  know- 
ledge. All  systems  of  philosophy,  especially  all  theories  of  on- 
tology, are  based  upon,  and  throughout  take  form  from,  certain 
definite  assumptions  in  respect  to  this  one  problem.  Realism, 
materialism,  and  idealism  in  all  its  varied  forms  and  develop- 
ments, commence  in  fact  with  the  question,  What  can  we 
know  ?  and  are  wholly  constructed  in  accordance  with  certain 
definite  answers  to  this  one  question,  answers  assumed  as  true. 
The  same  holds  true  of  all  the  deductions  of  these  systems  in 
respect  to  God,  duty,  immortality,  and  retribution. 

Now,  while  this  is  the  case,  no  philosopher,  we  believe,  has 
ever  attempted  to  give  us  a  formula  which  shall  undeniably  and 
self-evidently  represent  all  forms  of  valid  knowledge,  together 
with  the  certain  test  of  such  knowledge.     We  propose,  then, 


APPLIED     LOGIC.  323 

the  question,  What  is  this  formula,  as  the  first  and  great  prob- 
lem in  philosophy  in  the  present  age  ?  Till  this  problem  is 
solved,  it  is  self-evident  that  we  are  not  prepared  to  take  up  the 
other  great  questions  professedly  answered  in  these  various  sys- 
tems. The  language,  then,  which  Kant  applied  to  the  problem 
which  he  propounded  we  will  now  venture  to  apply  to  the  one 
before  us  :  "  All  metaphysicians  consequently  are  solemnly  and 
legally  suspended  from  their  occupations,  till  they  shall  have 
answered  in  a  satisfactory  manner  the  question,"  By  what 
formula  shall  we  represent  all  forms  of  valid  knowledge,  and 
what  is  the  certain  test  or  criteria  of  such  knowledge  ? 


PROPOSED    SOLUTION    OF   THIS   PROBLEM. 

To  the  question,  What  is  the  origin  of  knowledge  ?  many 
philosophers  have  propounded  many  and  different  answers ; 
but  to  the  question  now  before  us,  none,  to  our  knowledge, 
have  even  attempted  to  give  a  specific  answer.  To  the  follow- 
ing proposed  solution  of  this  problem  special  attention  is  now 
invited. 

Distinction  between  Presentative  and  Representative  Know- 
ledge. 

As  preparatory  to  the  solutior,  we  would  restate  a  distinction 
made  in  a  previous  department  of  this  treatise  between  presen- 
tative and  representative  knowledge.  We  will  give  the  dis- 
tinction in  the  language  of  Sir  William  Hamilton  : 

"  1.  A  thing  is  known  immediately  or  proximately  when  we 
cognize  it  in  itself;  mediately  or  remotely,  when  we  cognize  it 
in  or  through  something  numerically  different  from  itself.  Im- 
mediate cognition — thus  the  knowledge  of  a  thing  in  itself — in- 
volves the  fact  of  its  existence ;  mediate  cognition — t^us  the 
knowledge  of  a  thing  in  or  through  something  not  itself — in- 
volves only  the  possibility  of  its  existence. 

"  2.  An  immediate  cognition,  inasmuch  as  the  thing  known  is 
itself  presented  to  observation,  may  be  called  a  presentative  / 


324  LOGI'C. 

and  inasmuch  as  the  thing  presented  is,  as  it  were,  viewed  by 
the  mind  face  to  face,  may  be  called  an  intuitive  cognition.  A 
mediate  cognition,  inasmuch  as  the  thing  known  is  held  up  or 
mirrored  to  the  mind  in  a  vicarious  representation,  may  be 
called  a  representative  cognition. 

"  3.  A  thing  known  is  called  an  object  of  knowledge. 

"  4.  In  a  presentative  or  immediate  cognition  there  is  one  sole 
object ;  the  thing  (immediately)  known  and  the  thing  existing 
being  one  and  the  same.  In  a  representative  or  mediate  cog- 
nition there  may  be  discriminated  two  objects ;  the  thing  (im- 
mediately) known  and  the  thing  existing  being  numerically  dif 
ferent." 

That  we  have  these  two  kinds  of  knowledge  no  one  does  or 
can  doubt.  Of  some  realities,  to  say  the  least,  we  have  a  direct 
and  immediate  knowledge.  Of  other  realities  our  knowledge 
is  not  direct  and  immediate,  but  indirect  and  mediate.  All 
forms  of  mediate  knowledge,  as  all  admit,  are  originally  given 
through  one  source,  sensation.  We  shall  employ  the  words 
presentative  knowledge  to  represent  knowledge  of  the  first 
kind,  and  representative  for  that  of  the  second. 

In  addition  to  these  two  kinds  of  knowledge,  we  have  two 
other  kinds  also,  which  have  the  same  validity  as  these,  to  wit : 
those  truths  which  are  necessarily  presupposed  by  these  as  their 
logical  antecedents,  and  those  which  necessarily  result  from 
them  as  logical  consequences.  All  that  is  logically  presupposed 
and  which  logically  follows  from  any  form  of  knowledge,  must 
undeniably  have  the  same  validity  that  the  latter  does.  No 
one  will  or  can  doubt  the  truth  of  this  principle. 

The  formula  stated. 

We  are  now  prepared  to  give  a  distinct  statement  of  the 
formula  above  suggested.  It  is  this.  Presentative  knowledge, 
with  all  its  logical  antecedents  and  consequences,  must  be  held 
as  universally  and  absolutely  valid  for  the  reality  and  charac- 
ter of  the  objects  to  which  it  pertains. 

Representative  knowledge,  with  its  logical  antecedents  and 


APPLIED     LOGIC.  325 

consequences,  must  be  held  as  relatively  valid.  In  the  con- 
sciousness of  a  sensation,  for  example,  we  at  once  recognize  the 
fact  that  it  had  a  cause — a  cause  adequate  and  adapted  while 
we  remain  constituted  as  we  are,  and  that  cause  sustains  its 
present  relations  to  us,  to  affect  us  as  it  now  does.  So  far  our 
knowledge  of  that  cause,  with  all  that  is  necessarily  implied  in 
its  existence,  must  be  held  as  having  the  same  validity  that  our 
knowledge  of  the  sensation  has. 

.  The  test,  the  criteria  by  which  we  are  to  determine  whether 
any  given  form  of  knowledge  is  presentative  or  representative, 
is  consciousness.  If  we  are  conscious  of  a  direct  and  imme- 
diate perception-  of  any  object  whatever,  we  must  admit  the 
fact  that  our  knowledge  of  that  object  is  presentative.  If  we 
are  conscious  of  knowing  the  object  through  the  medium  of 
sensation,  then  our  knowledge  of  said  object  must  be  held  as 
representative. 

The  question  whether  any  particular  cognitions  must  be  held 
as  absolutely  valid  for  the  reality  and  character  of  its  object, 
will  in  reality  stand  thus : 

Presentative  knowledge,  with  its  logical  antecedents  and  consequences,  is 
universally  and  absolutely  valid  for  the  real  nature  and  character  of  its 
objects  ; 

These  cognitions  are  or  are  not  constituted  of  this  one  form  of  knowledge. 
Proof — consciousness  ; 

These  cognitions  consequently  are  or  are  not  thus  valid. 

The  syllogism  of  representative  knowledge  will  stand  thus : 

Kepresentative  knowledge,  with  its  logical  antecedents  and  consequences, 
is  universally  valid  for  the  relative  character  of  its  respective  objects. 

These  cognitions  are  or  are  not  constituted  of  this  form  of  knowledge. 
Proof — consciousness. 

Therefore  it  is  or  is  not  thus  valid. 

As  all  cognitions  are  in  fact  presentative  or  representative, 
these  formulas  must,  of  necessity,  include  all  forms  of  know- 
ledge. The  only  question  which  here  arises  is  this  :  Are  these 
formulas  themselves  really  valid  for  the  high  purpose  here  as- 
signed to  them  ?  That  they  are,  we  argue  from  the  following 
considerations : 


These  Formulas  and  Test  verified. 

1.  We  must  admit  their  absolute  and  universal  -validity,  or 
deny  that  of  all  knowledge  of  every  kind.  Presentative  is,  in 
fact,  the  highest  form  of  knowledge  of  which  we  can  by  any 
possibility  form  any  conception.  Its  validity  can  be  denied  on 
but  one  condition,  the  impeachment  of  the  integrity  of  the  in- 
telligence itself,  as  a  faculty  of  knowledge,  and  pronouncing  the 
idea  of  valid  knowledge  on  any  subject  whatever  an  absolute 
chimera. 

2.  No  other  formulas  and  test  besides  these  are  even  con- 
ceivable. We  must,  consequently,  admit  their  validity,  or  af- 
firm, that  if  valid  and  invalid  cognitions  do  exist,  we  have  no 
criteria  by  which  we  can  distinguish  one  class  from  the  other. 
Those  who  deny  the  validity  of  these,  are  bound  to  furnish 
some  others  possessing  really  valid  claims.  This,  we  are  quite 
confident,  they  will  never  even  attempt  to  do. 

3.  Every  form  and  system  of  knowledge,  as  a  matter  of  fact, 
admits  the  validity  of  these  formulas  and  test  in  certain  cases 
— in  all  cases  where  they  profess  to  find  valid  knowledge — and 
all  profess  to  find  such  as  far  as  their  own  fundamental  princi- 
ples and  deductions  are  concerned.  No  one  will  deny  these 
statements.  Now  the  validity  of  these  formulas  and  test  is  to 
be  admitted  universally  or  denied  universally.  If  one  form  of 
knowledge  given  in  consciousness  as  presentative,  and  for  the 
reason  that  it  is  thus  given,  is  to  be  received  as  valid  for  the 
nature  and  character  of  its  object — and  all  admit  that  some 
forms  thus  given  are  thus  valid,  and  none  pretend  that  any 
form  not  thus  given  is  thus  valid,  nor  that  any  form  of  know- 
ledge can  be  valid  for  any  other  reason — if  any  form  of  know- 
ledge given  in  consciousness  as  presentative,  is,  we  say,  for  the 
reason  that  it  is  thus  given,  to  be  regarded  as  valid,  every  other 
form  thus  given  must  be  regarded  as  thus  valid,  or  we  make  a 
discrimination  without  a  difference,  and  assume  that  things 
equal  to  the  same  things  may  not  be  equal  to  each  other. 
With  these  considerations,  the  subject  is  left  to  the  reflection 
of  the  thoughtful  reader. 


APPLIED     LOGIC.  327 

Searing  of  these  Formulas  upon  Systems  of  Ontology. 

\ 
In  the  human  intelligence  two  orders  of  cognitions  appear, 

the  subjective  and  objective — those  pertaining  to  mind,  on  the 
one  hand,  and  those  pertaining  to  matter  or  the  external  uni- 
verse, on  the  other.  The  great  problem  in  philosophy  for  all 
ages  has  pertained  to  the  question  of  the  validity  of  such  cog- 
nitions. In  view  of  the  formulas  and  test  under  consideration, 
but  one  answer  can  be  given  to  this  question.  No  one  will 
deny,  that  if  presentative  knowledge  must  be  held  as  universal- 
ly valid  for  the  reality  and  character  of  its  object,  then  the  uni- 
verse of  matter,  on  the  one  hand,  and  of  mind,  on  the  other, 
must  be  held  as  distinct  and  separate  realities — the  one  having 
real  and  absolute  extension  and  form,  and  the  other  as  a  sub- 
stance possessed  of  the  faculties  of  thought,  feeling,  and  volun- 
tary activity.  That  we  have  a  distinct  and  absolute  conscious- 
ness of  a  presentative  knowledge  of  each,  as  such  realities,  no 
one  will  deny.  The  validity  of  our  subjective  or  objective  cog- 
nitions for  the  reality  and  character  of  their  respective  objects 
can,  by  no  possibility,  be  denied,  but  upon  one  condition  exclu- 
sively— the  denial  of  the  validity  of  the  formula,  that  presenta- 
tive knowledge,  with  its  logical  antecedents  and  consequences, 
shall  be  held  as  universally  valid  for  the  reality  and  character  of 
its  objects.  Those  who  make  this  denial  can  maintain  their 
integrity  but  by  a  total  denial  of  the  fact,  that  we  have  or  can 
have  valid  knowledge  in  respect  to  any  subject  whatever. 

Character  and  claims  of  Empiricism,  Materialism,  Idealism, 
and  Realism,  as  systems  of  philosophy . 

Empiricism,  which  affirms  that  all  our  knowledge  is  derived 
directly  and  immediately  from  experience  (external  and  inter- 
nal perception) — materialism,  which  affirms  matter  to  be  the 
only  substance  really  existing — idealism,  which  affirms  mind  or 
its  operations  to  be  the  only  realities,  and  consequently  denies 
the  reality  of  an  external  material  universe — and  realism  as 
above  presented — realism,  which  affirms  the  reality  of  matter, 


328  logic. 

on  the  one  hand,  and  of  mind,  on  the  other,  and  asserts  the 
reality  of  the  two  as  distinct,  separate,  and  opposite  orders  of 
existences,  embrace  all  conceivable  or  possible  systems  of  phi- 
losophy. Of  empiricism  and  realism,  one  must  be  true  and  the 
other  false.  That  we  have  empirical  cognitions  both  systems 
affirm.  That  the  d  priori  element  of  thought  exists  as  a  matter 
of  fact,  the  former  theory  denies  and  the  latter  affirms.  One 
of  these  theories,  consequently,  must  be  time  and  the  other 
false.  As  far  as  the  question  of  ontology  is  concerned,  but 
three  systems  are  conceivable  or  possible,  and  one  of  these  to 
the  exclusion  of  the  others  must  be  true — to  wit,  materialism, 
idealism,  or  realism  which  affirms  the  reality  of  matter  and 
spirit  both.  Let  us  contemplate  the  character  and  claims  of 
these  systems. 

In  regard  to  empiricism,  we  would  remark,  that  it  admits  the 
validity  of  presentative  knowledge  as  far  as  the  empirical,  but 
denies  its  validity  as  far  as  the  d  priori,  elements  of  thought  are 
concerned.  Now  we  are  just  as  conscious  of  the  presence  in 
the  intelligence  of  one  of  these  elements  of  thought,  as  we  are 
of  the  other.  In  other  words,  we  are  just  as  conscious  of  the 
presence  in  the  intelligence  of  necessary  and  universal  ideas  and 
principles — such,  for  example,  as  the  ideas  of  space,  time,  sub- 
stance, cause,  personal  identity,  &c,  and  of  the  principles, 
"Body  supposes  space," — "Succession,  time," — "Phenomena, 
substance," — "  Events  a  cause,"  <fcc,  as  we  are  of  the  ideas  of 
body,  succession,  events,  &c.  Empiricism,  therefore,  affirms 
the  validity  of  presentative  knowledge  so  far  forth  as  the  em- 
pirical or  contingent,  and  denies  its  validity  so  far  forth  as  the 
d  priori  or  necessary,  element  of  thought  is  concerned. 

Materialism,  in  all  its  forms  and  developments,  rests  wholly 
upon  the  assumption  that  presentative  knowledge  Avith  its  logi- 
cal antecedents  and  consequences  is  valid  for  the  reality  and 
character  of  its  objects,  so  far  forth  as  external  perception  (ob- 
jective cognitions),  and  not  thus  valid,  so  far  as  internal  per- 
ception (subjective  cognitions)  are  concerned.  No  one  can 
deny,  that  we  are  just  as  conscious  of  knowing  ourselves  as 
substances  exercising  the  functions  of  thought,  feeling,  and  vo- 


APPLIED     LOGIC.  329 

lition,  as  we  are  of  knowing  matter  as  a  substance  having  ex- 
tension and  form.  Each  reality  is  alike,  and  with  equal  abso- 
luteness, given  in  consciousness  as  the  object  of  presentative 
knowledge.  Taking  the  principle,  that  phenomenon  supposes 
substance,  together  with  its  necessarily  implied  one,  that  sub- 
stances are  as  their  presentative  phenomena,  and  the  doctrine, 
that  matter  and  mind  are  real  existences  fundamentally  distinct 
and  separate  from  each  other,  is  just  as  demonstrably  evident 
as  any  of  the  deductions  of  the  mathematics.  Materialism  rests 
exclusively  upon  the  assumption,  we  repeat,  that  presentative 
knowledge,  with  its  logical  antecedents  and  consequences,  is 
valid  for  the  reality  and  character  of  its  objects  so  far  as  exter- 
nal material  substances  are  concerned,  and  not  thus  valid  in  re- 
gard to  mind,  and  must  stand  or  fall  with  the  claims  of  that 
assumption.  The  materialist  must,  to  maintain  his  integrity, 
abandon  his  theory  entirely  or  give  a  satisfactory  answer  to  the 
question,  Why  is  the  same  identical  form  of  knowledge  to  be 
regarded  as  valid  for  the  reality  and  character  of  one  class  of 
facts,  and  not  as  thus  valid  for  those  of  another  ? 

Idealism,  in  all  its  forms,  rests  upon  the  assumption,  that  pre- 
sentative knowledge,  with  its  logical  antecedents  and  conse- 
quences, is  valid  for  the  reality  and  character  of  the  facts  of  in- 
ternal perception  (subjective  cognitions),  and  not  thus  valid  for 
the  reality  and  character  of  the  facts  of  external  perception 
(objective  cognitions).  This  theory  is  throughout  nothing  but 
the  opposite  pole  of  the  same  assumption  on  which  materialism 
rests,  and  is  encumbered  in  all  its  principles  and  deductions, 
with  the  same  identical  difficulties,  to  wit :  that  the  same  iden- 
tical form  of  knowledge  is  valid  for  the  reality  and  character  of 
one  class  of  cognitions,  and  not  for  those  of  another — that  is, 
that  things  equal  to  the  same  things  are  not  universally  equal 
to  one  another.  We  are  just  as  undeniably  conscious  of  a  pre- 
sentative knowledge  of  matter  as  possessed  of  extension  and 
form,  as  we  are  of  .a  similar  knowledge  of  mind  as  exercising 
the  functions  of  thought,  feeling,  and  voluntary  determination, 
and  in  respect  to  each,  alike  and  equally,  that  knowledge  is  un- 
deniably absolute.    The  idealist,  then,  in  common  with  the  ma- 


terialist  must,  to  maintain  his  integrity,  abandon  his  theory  en- 
tirely or  give  a  satisfactory  answer  to  the  question,  Why  does 
he  assume  that  the  same  identical  form  of  knowledge  is  valid 
for  the  reality  and  character  of  the  objects  of  one  class  of  cog- 
nitions, and  not  valid  at  all  relatively  to  those  of  the  objects 
of  another  class  of  cognitions  ?  We  affirm  that  his  theory  is 
in  fact  based  upon  the  assumption,  that  the  principle,  "That 
things  equal  to  the  same  things  are  equal  to  one  another,"  is 
not  universally  valid  and  must  be  held  as  false,  if  this  principle 
must  be  held  as  true. 

Let  us  now  turn  our  attention  to  a  consideration  of  the  sys- 
tem of  realism,  as  we  have  above  presented  it — the  only  con- 
ceivable system  aside  from  those  above  noticed.  On  this  sys- 
tem we  remark : 

1.  It  is  based,  in  all  its  principles  and  deductions,  upon  the 
principle,  that  the  formulas  and  test  above  given  are  absolutely 
valid  throughout  the  entire  sphere  of  their  applications.  What- 
ever form  of  knowledge  is  given  in  consciousness  as  presenta- 
tive  or  representative,  it  recognizes  as  such,  and  together  with 
all  its  logical  antecedents  and  consequences,  as  absolutely  or 
relatively  valid  for  its  objects,  according  as  it  falls  under  one  or 
the  other  of  these  categories. 

2.  In  common  with  empiricism,  it  recognizes  the  reality  of 
the  empirical  or  contingent  elements  of  thought.  In  opposition 
to  the  former,  however,  it  recognizes  also  the  d  priori  or  neces- 
sary element.  It  recognizes  both  alike  as  real,  because  both 
alike  are  given  in  consciousness  as  such— that  is,  both  alike  are 
given  as  objects  of  presentative  knowledge. 

3.  By  recognizing  the  reality  and  validity  of  these  two  ele- 
ments of  thought,  it  lays  the  foundation  for  all  the  sciences  just 
as  they  are,  and  also  for  the  most  satisfactory  explanation  of 
their  possibility.  By  abstracting  the  d  priori  (necessary  and 
universal)  element  of  thought,  and  finding  its  logical  conse- 
quences, we  have  the  pure  sciences  as  they  are — those  of  the 
pure  mathematics,  for  example.  Blending  the  two,  and  ex- 
plaining the  facts  of  the  universe  in  the  light  of  d  priori  or  in- 


APPLIED     LOGIC.  331 

tuitive  principles  and  deductions,  we  have  the  mixed  sciences, 
physical  and  mental,  as  they  are. 

4.  In  contradiction  to  materialism  and  idealism  both,  this 
system  recognizes  the  reality  of  the  universe  of  matter  in  oppo- 
sition to  mind,  on  the  one  hand,  and  that  of  mind  in  opposition 
to  matter,  on  the  other ;  and  this  because  that  each  alike  and 
equally  is  given  in  consciousness  as  the  object  of  presentative 
knowledge. 

5.  Instead,  we  remark  finally,  of  giving  us  an  exclusively  ma- 
terial universe  with  no  deity  to  preside  over  it,  or  a  mere  ideal 
one  presided  over  by  an  ideal  divinity,  this  system,  in  its  ulti- 
mate necessary  logical  deductions,  gives  us  a  real  universe,  ma- 
terial and  mental — a  universe  presided  over  by  a  real  deity  who 
is  nothing  less  than  an  infinite,  eternal,  all-perfect,  self-conscious 
personality. 

General  Remarks  upo7i  these  Systems. 

Such  are  the  specific  character  and  claims  of  these  different 
and  opposite  systems.  We  would  now  invite  attention  to  a 
few  general  remarks  upon  them  :  y 

1.  Realism,  as  we  have  expounded  the  system,  is  really  and 
truly  based  upon  all  the  facts  of  consciousness,  while  each  of 
the  others  is  undeniably  a  system  of  partialism  recognizing 
but  a  part  of  these  facts,  while  all  alike  have  absolute  and  equal 
claims  to  validity.  All  forms  of  presentative  and  representative 
knowledge,  with  all  their  logical  antecedents  and  consequences, 
have  their  proper  place  in  the  system  first  named,  while  the  va- 
lidity of  a  part  of  said  forms  of  knowledge  is  admitted,  and  that 
of  another  part  denied  by  each  of  the  other  systems ;  and  all 
this  while  no  reasons  whatever  exist  for  the  fundamental  dis- 
tinctions which  are  made. 

2.  Realism  has  undeniably  a  truly  scientific  basis  and  struc- 
ture throughout,  inasmuch  as  all  its  foundation-principles  are 
universally  necessary  intuitive  truths,  and  all  its  subsequent  de- 
ductions are  exclusively  the  logical  consequences  of  such  princi-    <y 
pies,  and  the  actual  facts  of  consciousness.     The  formulas  and 


332  logic. 

test  above  given  which  lie  at  the  basis  of  this  system,  have  the 
same  claims  to  the  place  claimed  for  them  as  principles  of  sci- 
ence, that  any  other  principles  that  can  be  named  have  or  can 
have.  From  the  facts  of  consciousness  elucidated  by  these  prin- 
ciples, all  the  deductions  of  this  system  possess  a  demonstrative 
certainty.  On  the  other  hand,  the  principles  on  which  every 
one  of  the  other  systems  rests  are  nothing  but  mere  assump- 
tions, whose  validity  is  neither  intuitively  certain  nor  capable 
of  being  established  by  a  process  of  scientific  deduction.  Each 
of  these  systems,  as  we  have  seen,  rests  upon  the  assumption 
that  one  class  of  presentative  cognitions  is,  and  another  is  not, 
valid  for  the  reality  and  character  of  its  objects,  and  cannot 
itself  be  true  unless  that  assumption  is  valid.  Is  the  truth  of 
that  assumption  intuitively  certain  ?  No  one  will  assert  or  con- 
jecture that  it  is.  Can  its  validity  be  established  by  any  pro- 
cess of  scientific  deduction  ?  The  universal  intelligence  an- 
swers, No.  Neither  of  these  systems,  therefore,  have  or  can 
have  a  scientific  basis  ;  nor  can  any  of  its  deductions  have  any 
legitimate  claim  to  a  place  as  truths  of  science  in  any  of  our 
systems  of  knowledge. 

3.  Realism,  we  remark  in  the  last  place,  gives  us  in  its  prin- 
ciples and  deductions,  systems  of  real  valid  knowledge  in  re- 
gard to  ourselves,  to  the  world  and  God,  while  each  of  the  op- 
posite systems  utterly  unsettles  the  foundations  of  knowledge 
on  all  these,  and  all  other  subjects  alike,  if  there  be  any  other. 
In  the  one  case,  the  foundation  of  our  system  of  knowledge  is 
the  rock  of  truth,  absolute  intuitive  principles,  and  the  whole 
superstructure  rises  before  us  as  throughout  constituted  of  cor- 
responding materials.  In  each  of  the  other  cases,  we  commence 
with  a  formal  impeachment  of  the  validity  of  the  intelligence 
itself  as  a  faculty  of  knowledge — that  is,  with  a  formal  displace- 
ment of  the  foundations  of  valid  knowledge.  What  logically 
follows,  consequently,  can  have  no  higher  claims  to  validity. 
With  these  suggestions  these  systems  are  handed  over  to  the 
careful  reflection  of  inquirers  after  truth. 


APPLIED     LOGIC.  333 

DOGMATISM,    SKEPTICISM,    POSITIVEISM.    AND    FREE-THINKING. 

Dogmatism  and  skepticism  are  terms  in  frequent  use — terms 
which  require  specific  definition,  inasmuch  as  they  represent 
two  distinct  and  opposite  systems  of  belief,  systems  which  are 
not  very  clearly  apprehended  even  by  educated  minds  general- 
ly. The  system  represented  by  the  former  term  is  based  upon 
the  principle,  that  the  facts  of  the  universe,  material  and  men- 
tal, as  given  in  the  intelligence,  are  of  such  a  nature  as  to  affirm 
positively  a  certain  definite  system  of  belief,  and  to  deny  as 
positively  every  opposite  system,  and  hence  positively  requires 
us  to  hold  this  one  form  of  belief  as  true,  and  all  opposite  ones 
as  false.  In  opposition  to  this  principle,  skepticism  affirms  that 
the  entire  facts  under  consideration  are  of  such  a  nature  as  to 
admit  of  an  equally  consistent  explanation  in  full  and  perfect 
harmony  with  several  distinct  and  opposite  systems,  such  as 
realism,  materialism,  and  idealism  in  its  various  forms.  Such 
facts,  consequently,  simply  indicate  each  of  these  various  sys- 
tems alike  as  possibly  true,  with  the  absolute  impossibility  of  a 
valid  determination  which,  in  distinction  from  the  others,  is 
true.  Realism,  materialism,  idealism,  theism,  atheism,  &c,  are 
all  dogmatic  systems,  because  each  of  them  holds  a  certain  form 
of  belief  as  positively  affirmed  as  true,  and  all  opposite  ones  as 
false,  by  the  facts  of  the  universe.  Skepticism  affirms  of  each 
system  alike,  This  system  may  or  may  not  be  true,  and  by 
no  possibility  can  it  be  determined  whether  it  is  or  is  not  true, 
and  hence  condemns  the  dogmatism  of  each  alike,  that  is,  de- 
nies the  claims  of  each  alike  to  be  held,  in  distinction  from  the 
others,  as  true. 

Skepticism,  it  will  readily  be  perceived,  is,  in  fact,  as  a  sys- 
tem, as  really  and  truly  dogmatic  as  either  of  the  others,  but  in 
a  different  form.  To  the  facts  of  the  universe  it  gives  an  ex- 
planation as  positive  as  they.  While  they  assert  that  these 
facts  do  affirm  one  system,  in  distinction  from  all  others,  as 
true,  it  as  positively  and  dogmatically  affirms  that  said  facts 
simply  suggest  various  systems,  and  each  as  possibly  true,  with 
the  absolute  impossibility  of  determining  whether  any  one  sys- 


334  logic. 

tern  is  or  is  not  true.  In  opposition  to  the  dogmatic  teachings 
of  these  systems,  skepticism  as  dogmatically  affirms,  You  can- 
not prove  that<  there  is  an  external  world,  nor  that  such  a  world 
does  not  exist — you  cannot  prove  that  there  is  a  God,  nor  that 
there  is  not  a  God,  &c. 

Positiveism  and  free-thinking  are  terms  nearly  synonymous 
in  their  meaning  with  those  already  considered,  and  may  be 
considered  as  representing  them  in  their  practical  principles  or 
developments.  The  categorical  imperative  of  positiveism  is, 
Thou  shalt  hold  this  specific  system  as  true,  and  all  opposite 
and  contradictory  ones  as  false.  That  of  free-thinking  is,  Thou 
mayest  assume  any  of  these  hypotheses  you  please  as  true,  and 
explain  the  facts  of  the  universe  accordingly,  provided  you  hold 
said  hypothesis  as  only  possibly  true,  and  do  not  dogmatically 
impose  it  upon  others.  The  imperative  of  positiveism  has  place 
where,  and  only  where,  the  facts  presented  positively  affirm  one 
hypothesis,  and  are  explicable  on  no  other,  that  is,  positively 
contradict  every  other.  That  of  free-thinking  has  place  where, 
and  only  where,  the  facts  presented  suggest  two  or  more  dis- 
tinct and  opposite  hypotheses,  as  each  possibly  true,  and  equal- 
ly so,  without  indicating  or  affirming  either  in  distinction  from 
the  others  as  true. 


CONDITIONS    OF   THE    POSSIBILITY    OF   SCIENCE   IN   ANY    PARTICU- 
LAR  DEPARTMENT    OF   THOUGHT. 

We  are  now  prepared  to  state  definitely  the  conditions  on 
which  real  science,  in  any  particular  department  of  thought  is 
possible.     They  are  the  following : 

1.  The  facts  presented  in  said  department  must  yield  certain 
specific  analytical  judgments — that  is,  certain  universal  and 
necessary  intuitive  truths  under  which  all  such  facts  may  be 
ranged,  and  in  the  light  of  which,  as  principles,  said  facts  may 
be  explained. 

2.  Said  facts  must  sustain  certain  fixed,  determinate,  and  de- 
terminable relations  to  each  other — relations  the  same  in  kind 
as  those  represented  in  the  principles  under  consideration.     If 


APPLIED     LOGIC.  335 

the  relations  determined  were  not  the  same  in  kind  as  those 
designated  by  the  principles  above  presented,  the  former  would 
not  be  ranged  under  the  latter,  and  no  inferences  or  deductions 
would  be  yielded. 

'  3.  These  principles  and  relations  must  yield  important  de- 
ductions, which,  as  principles,  will  yield  ethers,  and  so  on  till 
the  mass  of  facts  referred  to  stand  before  us  distinctly  eluci- 
dated. 

In  illustration  of  these  statements,  we  may  refer  to  the  sci- 
ence of  geometry.  The  ideas  of  quantity  which  it  is  the  object 
of  this  science  to  elucidate,  present,  first  of  all,  certain  analyti- 
cal judgments  which  may  be  employed  as  scientific  principles — 
the  principles,  for  example,  "  Things  equal  to  the  same  things 
are  equal  to  one  another," — "  If  equals  be  added  to  equals  the 
sums  are  equal,"  &c.  Then  these  quantities,  when  defined  as 
lines  and  figures,  are  found  to  sustain  certain  determinable  rela- 
tions to  each  other — relations  the  same  in  kind  as  those  desig- 
nated by  the  principles  referred  to — as,  A  and  B  are  each  equal 
to  C.  These  relations,  in  the  light  of  those  principles,  yield 
certain  important  deductions — as,  A  and  B  are  equal  to  one 
another — deductions  which,  as  principles,  lead  to  others,  and 
so  on  till  our  ideas  of  quantity  stand  before  us  distinctly  eluci- 
dated. All  these  conditions  must  be  fulfilled  in  any  given  de 
partment  of  thought,  or  science  there  is  an  impossibility. 

Bearings  of  the  Sensational  Theory  of  Perception. 

As  preparatory  to  discussions  hereafter  to  be  introduced,  we 
would  now  re-direct  attention  to  the  necessary  deductions  and 
consequences  of  the  sensational  theory  of  external  perception. 
According  to  the  fundamental  assumptions  of  this  theory,  of  an 
external  world,  if  it  exists  at  all,  we  have  no  real  perception 
whatever,  the  sensation  itself,  a  purely  and  exclusively  mental 
state,  being  the  only  object  which  we  really  perceive,  when  we 
suppose  ourselves  perceiving  an  extended  object  external  to  the 
mind  itself.  Further,  according  to  the  fundamental  principles 
of  this  theory,  if  our  sensations  as  they  are  were  induced  from 


336  LOGIC. 

any  cause  whatever,  we  should  have,  from  the  nature  of  the  in- 
telligence itself,  the  same  identical  perceptions  and  subsequent 
mental  operations  that  we  now  do  have,  even  supposing  that  no 
external  world  at  all  exists,  or  no  external  cause  of  the  sensa- 
tion. All  that  we  can  know  of  the  actual  cause  of  the  sensation 
is  from  sensation  itself,  and  nothing  else.  Now  it  is  undenia- 
ble, that  sensation  contains,  and  can  contain,  within  itself  no 
indication  or  revelation  whatever  of  what  the  nature  of  that 
cause  is  or  must  be.  Of  a  thing  utterly  void  of  extension  and 
form,  we  cannot  say  that  its  cause  must  be  an  extended  sub- 
stance having  any  form  whatever,  much  less  a  definite  form. 
For  aught  that  we  know  or  can  thus  know,  that  cause  may  or 
may  not  be  an  external  extended  object  such  as  we  seem  to 
perceive.  Or  it  may  be  an  unknown  and  unknowable  some- 
thing according  to  the  theory  of  Kant.  Still  further,  for  aught 
revealed  in  and  by  sensation,  its  cause  may  not  be  any  external 
object  whatever,  but  wholly  ab  intra,  the  result  of  the  mind's 
spontaneous  activity,  according  to  the  theory  of  Fichte.  For 
aught  that  we  know  or  can  know  from  the  sensation  itself,  we 
remark  in  the  last  place,  its  cause  may  accord  with  the  assump- 
tions of  pantheism,  or  exist  as  a  mere  idea  according  to  the 
teachings  of  pure  idealism.  When  we  would  reason,  then, 
from  sensation  to  its  cause,  several  distinct  and  opposite  hy- 
potheses present  themselves,  each  equally  consistent  with  all  the 
facts  and  all  their  characteristics,  with  an  absolute  impossibility 
on  our  part  of  knowing  which,  in  distinction  from  the  others, 
is  true.  Yet  these  hypotheses  involve  perfectly  distinct  and 
opposite  deductions  in  regard  to  ourselves,  our  duty  and  desti  ■ 
ny,  the  world  and  God.  All  this  is  undeniable.  What  then  is 
the  necessary  logical  consequence  of  this  theory  ?  The  system 
of  absolute  skepticism,  in  accordance  with  our  explanation  of  it, 
and  nothing  else.  No  man  can  hold  this  theory  of  perception, 
and,  without  the  grossest  inconsistency  and  self-contradiction, 
be  any  thing  else  than  a  universal  skeptic  and  free-thinker. 


APPLIED     LOGIC.  33*7 


CONDITIONS  ON  WHICH  THE  PROPOSITION,  V  GOD  EXISTS,"  CAN 
LEGITIMATELY  TAKE  ITS  PLACE  AS  AN  UNDENIABLE  TRUTH 
OP   SCIENCE. 

We  would  now  invite  very  special  attention  to  the  following 
question,  to  wit :  On  what  conditions  can  the  theistic  proposi- 
tion, "  God  exists,"  legitimately  take  rank  as  an  undeniable 
truth  of  science  ?  In  other  words,  On  what  conditions  can  the 
validity  of  that  proposition  be  established  on  scientific  grounds  ? 
They  are  the  following  : 

1.  An  analytical  judgment  in  respect  to  the  facts  of  the  uni- 
verse must  be  presented,  a  judgment  having  such  intuitive,  ab- 
solute, and  necessary  certainty,  that  no  one,  not  even  the  skep- 
tic or  anti-theist,  will  or  can  deny  it ;  a  judgment,  too,  necessa- 
rily involving  the  validity  of  the  theistic  hypothesis  of  ultimate 
causation,  on  the  supposition  that  the  facts  of  the  universe 
do  accord  really  and  truly  with  that  principle.  This  judg- 
ment will  stand  as  the  major  premise  of  the  theistic  syllogism. 
About  the  question  of  its  validity  as  a  scientific  principle  there 
must  be  no  dispute. 

2.  As  the  minor  premise,  it  must  be  shown  undeniably  that 
the  facts  of  the  universe  bearing  upon  this  question  do  really 
and  truly  accord  with  this  principle,  and  thus  affirm  the  validity 
of  this  hypothesis  as  a  matter  of  fact. 

3.  The  necessary  deduction  from  these  premises,  to  wit, 
"  God  exists,"  then  legitimately  takes  its  place  as  a  truth  of 
science.     On  no  other  conditions  is  this  possible. 

The  same  conditions  hold  in  regard  to  all  other  deductive  or 
inductive  truths.  Long  before  the  science  of  geometry  or  of 
the  mathematics  in  any  form,  for  example,  was  developed,  all 
men  Avould  conclude,  from  the  fact  that  A  and  B  were  each 
equal  to  C,  that  they  were  equal  to  one  another — just  as  the 
general  intelligence  now,  from  its  spontaneous  activities,  affirms 
in  view  of  the  facts  of  the  universe  within  and  around  us,  the 
being  and  perfections  of  God.  Yet,  never  till  the  analytical 
judgment,  "Things  equal  to  the  same  things  are  equal  to  one 
another,"  was  distinctly  developed,  and  the  judgment,  "A  and 


V 


B  are  equal  to  C,"  was  specifically  arranged  under  the  above- 
named  principle,  could  even  the  deduction,  "  Therefore,  A  and 
B  are  equal  to  one  another,"  be  ranked  as  a  truth  of  science. 
So  of  the  great  truth  of  theology  under  consideration,  and  of 
every  other  inferred  truth. 

There  are  two  distinct  elements  of  the  theistic  proposition, 
"  God  exists,"  to  wit,  that  the  ultimate  unconditioned  cause  of 
the  facts  of  the  universe  is  a  power  out  of  and  above  nature, 
and  one  which  exercises  an  absolute  control  over  it — and  that 
this  cause  is  a  self-conscious  personality  possessed  of  all  the  at- 
tributes involved  in  the  ideas  of  absolute  infinity  and  perfection. 
Two  separate  formulas  may  be  required  to  represent  these  two 
distinct  elements  of  the  above-named  proposition.  We  will 
simply  indicate  what,  in  our  judgment,  would  be  formulas 
which  would  stand  as  undeniably  valid  majors  in  the  different 
forms  in  which  the  theistic  syllogism  should  be  presented — 
formulas  which  must  be  universally  regarded  as  possessing  ab- 
solute appodictical  certainty. 

The  Theistical  Formulas. 

1.  On  two  conditions  would  the  facts  of  the  universe  demon- 
strably affirm  the  truth,  that  the  unconditioned  cause  of  said 
facts  is  a  power  not  inhering  in,  but  out  of  and  above,  nature — 
the  supposition  that  the  order,  scientific  arrangement,  and  har- 
mony, mental  and  physical,  everywhere  existing  in  the  universe 
is  an  event  originated  in  time,  that  is,  a  reality  which  once  did 
not  exist  but  began  to  be — and  that  the  course  of  events  which 
has  been  in  progress  since  this  order  was  established  has  been, 
from  time  to  time,  interrupted  in  forms  which  can  be  accounted 
for  by  a  reference  to  no  inhering  law  of  nature.  This  cause 
must  of  necessity  be  a  law  inhering  in  nature  itself  and  acting 
potentially  and  necessarily  in  it,  or  a  power  out  of  and  above 
nature.  On  the  former  supposition,  the  order  of  creation  could 
by  no  possibility  be  an  event  originated  in  time,  but  must  have 
existed  from  eternity.  On  the  same  supposition,  also,  this  order 
could  never  from  eternity  to  eternity  be  interrupted  in  any 


APPLIED     LOGIC.  339 

form.  This  is  undeniable.  The  formulas  above  given,  on  the 
supposition  that  the  facts  of  the  universe  do  accord  with  them, 
will  of  necessity  yield  the  one  element  of  the  theistic  hypothe- 
sis under  consideration. 

2.  The  following  formula  would  as  necessarily  yield  the  other 
element  of  this  hypothesis,  the  infinity,  and  perfection  of  this 
cause,  to  wit,  that  universal  mind  is  so  constituted  as  of  neces- 
sity to  form  the  idea  of  this  cause  as  a  self-conscious  personality, 
possessed  of  all  the  attributes  involved  in  the  ideas  of  absolute 
infinity  and  perfection,  and  that  the  assumption  of  the  objective 
validity  of  that  idea  in  opposition  to  all  opposite  conceptions,  is 
an  immutable  demand  of  its  moral  and  spiritual  being.  The 
case  is  then  brought  under  the  universal  and  immutable  law,  a 
law  whose  validity  none  will  dare  to  deny,  to  wit,  that  for 
every  fundamental  want  of  sentient  existence  there  is  a  cor- 
related provision,  and  for  every  fundamental  adaption  a  corre- 
sponding reality  or  sphere  of  activity. 

It  will  then  remain  to  show  in  arguing  the  minor  premise, 
that  the  facts  of  the  universe  do  in  reality  accord  with  these 
two  formulas,  and  with  none  others.  The  necessary  deduction, 
"God  exists,"  will  then  undeniably  take  rank  as  a  truth  of 
science. 


The  Disjunctive  Argument  for  the  Theistic  Hypothesis. 

The  argument  for  the  theistic  hypothesis  may  be  presented 
in  another  form — the  disjunctive — in  which  form  it  will  possess 
the  most  absolute  validity.  There  are  but  three  conceivable 
hypotheses  of  ultimate  causation,  that  of  theism,  materialism, 
and  idealism  in  its  various  forms.  One  of  these  hypotheses  to 
the  exclusion  of  the  others  must  be  true.  Now  it  can  be  ren- 
dered demonstrably  evident,  that  the  entire  facts  of  the  uni- 
verse can  by  no  possibility  be  explained  in  consistency  with 
either  of  the  two  last  named — a  fact  which  renders  equally 
evident  the  validity  of  the  first.  This  form  of  the  theistic  argu- 
ment has  never  yet,  to  our  knowledge,  b^en  presented  in  its 


340  LOGIC. 

full  force,  and  has  for  the  most  part  been  entirely  overlooked 
by  the  advocates  of  theism. 

The  ultimate  principles  on  which  the  hypotheses  of  Theism, 
Skepticism,  and  Anti-Theism  in  all  its  forms,  rest. 

In  conducting  the  argument  under  consideration  on  right 
principles,  it  will  ultimately  be  found  that  the  following  are  the 
principles  on  which  theism,  on  the  one  hand,  and  all  opposite 
systems,  on  the  other,  finally  rest.  The  theistic  principle  is 
this  :  The  entire  facts  given  in  consciousness  as  the  real  objects 
of  presentative  knowledge,  are  all  alike  to  be  held  as  together 
constituting  a  valid  basis  for  absolute  deductions  in  respect  to 
the  nature  and  character  of  the  ultimate  unconditioned  cause  of 
the  facts  of  the  universe.  Every  hypothesis  opposed  to  that  of 
theism,  on  the  other  hand,  rests  upon  the  assumption,  that  a 
part  of  the  class  of  facts  under  consideration — that  part  which, 
if  admitted  as  constituting  the  whole  of  the  kind  that  do  exist, 
would  affirm  the  skeptical  or  anti-theistic  hypothesis  and  deny 
that  of  theism — are  to  be  held  as  valid  for  deductions  on  this 
subject ;  while  all  others  of  the  same  identical  class,  those  which, 
if  admitted,  would  affirm  the  theistic,  and  deny  every  opposite, 
hypothesis,  are  to  be  held  as  void  of  all  validity  as  the  basis  of 
such  deductions.  It  will  be  seen  that,  granting  the  validity  of 
the  principle  first  named,  theism  must  be  true,  and  that  upon 
no  other  condition  than  that  of  the  second,  can  any  opposite 
hypothesis  by  any  possibility  be  true.  The  validity  of  the 
theistic  hypothesis  has  never,  as  a  matter  of  fact,  been  denied  or 
doubted  but  upon  one  condition — a  denial  of  the  reality  of  the 
material,  on  the  one  hand,  or  of  the  mental  world,  on  the 
other,  or  of  both  together — that  is,  on  a  denial  of  the  validity 
of  our  knowledge  in  respect  to  matter,  or  mind,  or  of  both  to- 
gether. Materialism  denies  the  validity  of  all  knowledge  of 
mind — idealism  of  matter — and  skepticism  of  both  together, 
"so  far  as  any  valid  basis  for  positive  systems  of  knowledge  and 
belief  are  concerned.  Now  of  matter,  on  the  one  hand,  and 
of  miaad,  on  the  other,  we  are  conscious  of  having  a  real  presen- 


APPLIED     LOGIC.  341 

tative  knowledge.  Materialism,  then,  rests  upon  the  assump- 
tion, that  this  form  of  knowledge  is  valid  so  far  forth  as  the 
class  of  cognitions  pertaining  to  matter  is  concerned,  and  not 
valid  as  far  as  that  class  which  pertains  to  mind  is  concerned. 
Idealism,  as  the  basis  of  its  deductions,  affirms  the  validity  of 
the  latter  class,  and  denies  that  of  the  former. 

COMMON  THEISTIC    SYLLOGISM   AND   ARGUMENT. 

Hitherto,  with  very  few  exceptions,  what  has  been  called 
"  the  design  argument"  has  been  almost  exclusively  employed 
in  all  attempted  demonstrations  of  the  being  of  God.  The  prin- 
ciple on  which  the  argument  has  been  conducted  has  always 
been  one  and  the  same.  The  main  difference  which  has  charac- 
terized the  productions  of  different  authors,  has  been  the  class 
of  examples  of  design  which  has  been  adduced  as  the  basis  of 
specific  deductions.  The  validity  of  the  procedure  itself,  that 
is,  of  the  form  which  the  argument  has  assumed,  has  been  taken 
for  granted  as  self-evident.  The  time,  in  our  judgment,  has 
come  when  the  form  itself  of  the  argument  should  receive  a 
rigid  examination ;  and  this  because  its  validity  has  always  been 
positively  denied  by  anti-theists — is  now  seriously  questioned  by 
some,  at  least,  of  the  best  thinkers  among  theists — has,  as  far 
as  our  knowledge  extends,  failed  altogether  as  a  means  of 
convincing  unbelievers,  and  been  nearly,  if  not  quite,  equally 
inefficacious  in  confirming  the  faith  of  believers.  We  propose, 
then,  to  offer  a  few  brief  criticisms  upon  what  is  denomina- 
ted the  theistic  syllogism,  and  upon  the  form  of  argumenta- 
tion pursued  under  that  syllogism.  The  syllogism 'may  be  thus 
stated  : 

Marks  of  design,  that  is,  where  the  parts  of  any  given  whole 
are  so  arranged  as  to  accomplish  some  intelligible  purpose  or 
end — the  adjustment  of  the  parts  of  the  watch,  for  example,  so 
that  a  regulated  motion  which  points  out  the  hours  of  the  day, 
is  produced — imply  an  intelligent  designing  cause.  The  works 
of  nature  are  of  this  character.  They  therefore  imply  a  design- 
ing cause. 


342  logic. 

The  best  formal  statement  of  this  syllogism,  probably,  is  that 
given  by  Professor  Tulloch,  and  which  we  will  here  cite  again  : 
"  First  or  major  premise, 

Order  universally  proves  mind  ; 
Second  or  minor  premise, 

The  works  of  nature  discover  order  ; 
Conclusion, 

The  works  of  nature  prove  mind." 

In  regard  to  this  syllogism,  we  would  observe,  that  the  ma- 
jor premise  is  the  only  one  which  has  ever  been  disputed.  No 
skeptic  or  anti-theist  of  any  school  has  ever  questioned  the  truth 
of  the  statement,  that  "  The  works  of  nature  discover  order." 
The  validity  of  the  major,  however,  to  wit,  that  "  Order  uni- 
versally proves  mind,"  has  been  universally  denied  by  the  op- 
posers  of  theism,  while  its  right  to  a  place  as  a  first  truth  or 
principle  of  science  has,  as  we  have  said,  been  doubted  by  not 
a  few  leading  minds  among  theists  themselves.  While  this  has 
been  the  case,  the  minor  premise,  which  has  never  been  denied 
or  doubted  even,  has  been  almost  exclusively  argued — and  ar- 
gued, too,  as  if  it  was  the  only  one  which  is  doubted  or  denied. 
The  theistic  syllogism  and  argument,  then,  as  hitherto  almost 
exclusively  presented,  exhibits  the  following,  we  believe,  unex- 
ampled phenomena  in  the  history  of  science — to  wit,  a  syllogism 
with  a  disputed  major  and  an  admitted  minor ;  while  the  former 
has  been  assumed  as  a  universally  admitted  principle,  and  the 
latter  argued  as  the  only  disputed  premise.  "We  would  now 
invite  special  attention  to  the  following  suggestions  in  respect 
to  the  syllogism  and  argument  before  us. 

1.  The  order  of  the  premises  in  this  case  is,  in  one  funda- 
mental particular,  the  reverse  of  what  science  universally  de- 
mands— an  order  which  renders  scientific  development  in  the 
theistic  department  of  thought  unattainable.  In  all  the  sci- 
ences, the  major  is  never  allowed  to  be  a  disputed  premise. 
If  either  is  disputed,  it  must  be  the  minor,  and  that  only. 
Yet  here  we  have  a  disputed  major  and  an  admitted  minor. 


APPLIED     LOGIC.  343 

HoV  can  the  idea  of  science  be  realized  under  such  circum- 
stances ? 

2.  The  major  premise,  in  this  case,  is  not  only  not  what  sci- 
ence universally  requires  in  regard  to  the  major,  an  analytic 
judgment — that  is,  a  universal  and  necessary  intuitive  truth — 
but  a  problematical  proposition  requiring  proof  before  it  is  ad- 
mitted as  a  premise  at  all.  This  is  evident,  in  the  first  place, 
from  the  fact  that  its  validity  is  universally  denied  by  the  op- 
posers,  and  its  claims,  as  a  first  truth,  doubted  by  many  of  the 
advocates,  of  theism,  Professor  Tulloch,  for  example. 

That  such  is  the  character  of  this  premise  may,  we  would  re- 
mark in  the  next  place,  be  rendered  undeniably  evident,  by  the 
statement  of  a  few  self-evident  truths.  It  is  self-evident  that 
we  cannot  know  d  priori  what  kind  of  realities  or  substances 
do  or  do  not  exist.  For  aught  that  we  can  thus  know,  mat- 
ter and  spirit  both  may  have  existed  from  eternity.  On  the 
supposition,  that  either  has  existed  from  eternity,  we  cannot 
affirm  d  priori  in  what  state  it  may  have  existed,  whether 
in  a  state  of  order  or  not.  In  one  or  the  other  of  them  (mat- 
ter or  mind)  it  is  undeniable  that  order  must  have  existed  with- 
out a  cause,  and  we  cannot  affirm  d  priori  in  which  it  has, 
and  in  which  it  has  not,  thus  existed.  It  is  equally  as  conceiva- 
ble that  it  might  thus  have  existed  in  one  as  in  the  other.  No 
one  can  affirm  d  priori  that  this  is  not  the  case.  If,  then,  we 
consider  nature  as  having  existed  from  eternity — that  is,  un- 
caused— we  cannot  affirm  d  priori  that  it  might  not  have  exist- 
ed in  a  state  of  order,  and  that  order  the  result  of  no  cause  out 
of  and  above  nature.  The  proposition,  then,  "  Order  univer- 
sally proves  mind," — mind  as  its  originating  cause — is,  either 
not  in  its  absolutely  universal  form  true,  in  fact,  or  its  truth  in 
this  form  is  not  self-evident.  That  proposition,  consequently, 
has  no  claim  whatever  to  take  the  rank  assigned  to  it  in  the 
common  theistic  syllogism,  to  wit,  that  of  a  first  truth  or  princi- 
ple of  science.  It  is  only  in  the  form  in  which  we  have  stated 
it,  that  it  has  or  can  have  intuitive  certainty,  to  wit,  Order 
which  once  did  not  exist  and  began  to  be,  or  which  has,  from 
time  to  time,  been  interrupted  and  changed  in  forms  which  can 


be  accounted  for  by  a  reference  to  no  inhering  law  or  Ia^s  of 
nature — order  of  this  character  universally  supposes,  as  its  origi- 
nating cause,  a  power  out  of  and  above  nature,  that  is,  mind. 
This,  then,  and  not  that  above  given,  is  the  proper  major  in  the 
theistic  syllogism.     This  leads  us  to  remark  : 

3.  That  the  objections  urged  by  the  opposers  of  theism 
against  this  proposition  as  having  a  claim  to  the  rank  of  a  first 
truth  of  science,  the  place  assigned  it  in  the  syllogism  under 
consideration,  have  never,  to  our  knowledge,  been  satisfactori- 
ly answered,  and  they  are  in  our  judgment,  we  are  free  to  say, 
unanswerable.  These  objections  are  embodied  in  the  celebrated 
formula  of  Mr.  Hume,  which  is  in  substance  as  follows :  The 
supposition  of  an  eternally  existing  order  in  nature — an  order 
which  exists  without  a  cause — is  no  more  inconceivable  or  self- 
contradictory  than  that  of  the  eternal  existence  of  an  infinite 
mind — a  mind  capable  of  conceiving  of  the  order  existing  in 
nature  and  actually  establishing  it,  and  all  this  without  a  cause. 
No  individual  has  yet  shown  that  this  formula  is  not  self-evi- 
dently  true  ;  nor,  in  our  judgment,  can  any  one  do  it.  In  our 
development  of  the  principles  by  which  the  validity  of  objec- 
tions against  any  given  hypothesis  may  be  tested,  we  laid  down 
this  as  a  universal  principle,  that  no  objection  which-  exists  in 
full  force  against  a  proposition  known  to  be  true,  has  any  validi- 
ty when  arrayed  against  any  other  proposition.  Leaving  out 
of  view  the  idea  that  the  order  existing  in  nature  once  did  not 
exist  and  began  to  be,  every  objection  against  the  conception 
of  such  order  existing  without  a  cause,  lies  equally  against  the 
conception  of  the  being  and  perfections  of  God.  But  one  of 
these  must  be  true.  The  objection,  then,  is  void  of  validity 
against  either.  The  way,  and  the  only  way,  in  which  the  argu- 
ment of  Mr.  Hume  can  be  met,  is  by  showing  that  the  order 
actually  existing  in  nature  does  not  come  under  the  principle 
to  which  he  has  assigned  it,  but  falls,  in  fact,  under  a  very  dif- 
ferent principle — a  principle  which  necessarily  afiirms  the  theis- 
tic hypothesis,  on  the  supposition  that  the  order  existing  in  na- 
ture falls  under  that  principle. 

4.  Equally  valid,  in  our  judgment,  are  the  objections  urged 


APPLIED     LOGIC.  345 

by  Mr.  Hume,  Mill,  and  others,  against  the  proof  of  this  prin- 
ciple, as  adduced  by  theistic  writers.  "  If,"  says  Dr.  Chalmers, 
"  we  can  infer  the  agency  of  design  in  a  watchmaker,  though 
we  never  saw  a  watch  made,  we  can,  on  the  very  same  ground, 
infer  the  agency  of  design  on  the  part  of  a  world-maker,  though 
we  never  saw  a  world  made."  The  above  we  regard  as  strict- 
ly an  analytical  judgment.  It  is  impossible  even  to  conceive  of 
the  opposite  as  true.  The  reason  is  obvious.  There  is  here  a 
common  assumption  in  regard  to  the  two  cases — the  watch  and 
the  world — to  wit,  that  both  alike  were,  in  fact,  made,  that  is, 
once  did  not  exist  and  then  were  produced.  In  all  such  cases, 
we  can,  as  Dr.  Chalmers  shows,  legitimately  reason  from  the 
character  of  the'  thing  made  to  that  of  the  maker.  But  sup- 
pose we  do  know  that  the  watch,  and  do  not  know  that  the 
world,  was  made ;  in  other  words,  suppose  that  we  do  know 
that  the  order  and  arrangement  existing  in  the  watch  once  did 
not  exist,  and  began  to  be,  while  we  do  not  know  this  of  the 
order  and  arrangement  existing  in  nature.  The  cases  then  are 
not  at  all  parallel,  and  we  cannot,  reason  from  the  one  to  the 
other.  Let  us  suppose,  still  further,  that  the  order  and  arrange- 
ment existing  in  the  watch  are  not  only  known  to  be  an  effect 
originated  in  time,  but  to  be  of  such  a  nature  that  they  could, 
by  no  possibility,  have  been  produced  by  any  laws  inhering  in 
nature  itself,  while  we  do  not  and  cannot  know  that  the  order 
and  arrangement  existing  in  nature  ever  were  produced  at  all, 
that  is,  do  not  and  cannot  know  but  that  they  have,  in  fact, 
existed  from  eternity.  The  two  cases,  on  that  supposition,  not 
only  do  not  fall  together  under  the  same  inductive  syllogism, 
but  do  not  fall  under  that  of  analogy.  In  other  words,  they 
are  not  even  analogous  cases.  We  cannot  logically  reason  from 
a  case  which  we  know  must  have  been  produced  by  one  specific 
cause,  to  one  that  we  do  not  know  was  produced  by  any  cause 
whatever.  The  validity  of  this  principle,  Dr.  Chalmers  distinct- 
ly recognizes  in  his  "  Natural  Theology,"  affirming,  that  before 
we  can  reason  from  the  order  existing  in  nature  to  the  charac- 
ter of  God  as  the  cause  of  that  order,  we  must  show  that  the 
former  is,  in  fact,  an  effect,  that  is,  was  originated  in  time.  If 
15* 


0 


it  existed  from  eternity,  it  cannot  be  affirmed  to  be  an  effect  at 
all,  and  we  cannot  reason  from  it  to  any  cause  whatever. 
When  we  reason  from  the  mere  fact  of  order,  therefore,  irre- 
spective of  the  question  of  its  origin,  to  the  character  of  God, 
Ave  reason  most  illogically. 

There  are  events,  however,  that  we  know  were  produced  by 
a  designing  cause — the  watch,  for  example.  On  what  condition 
can  we  conclude  that  because  marks  of  design  or  facts  of  order 
here  imply  a  designing  cause,  that  marks  of  design  or  facts  of 
order  in  any  other  case  suppose  a  similar  cause  ?  On  this  con- 
dition exclusively,  that  the  facts  of  order  in  both  cases  are  the 
same  in  kind,  that  is,  belong  to  the  same  species.  If  we  have 
different  kinds  of  order,  we  cannot,  by  induction,  but  exclusive- 
ly on  the  principle  of  analogy,  reason  from  the  one  to  the  other, 
and  then  we  obtain  only  probable  deductions.  Now  Mr.  Mill, 
Hume,  and  others,  contend  that  when  we  reason  from  the  facts 
of  order  which  appear  in  the  watch  to  those  which  appear  in 
nature,  we  do  not  reason  from  one  individual  of  a  given  species 
to  another  of  the  same  species,  and  that  in  view  of  the  specifical 
element  common  to  the  two,  but  from  one  individual  of  one 
species  to  another  of  a  different  and  opposite  species,  and  this 
in  view  merely  of  the  generical  element  which  they  possess  in 
common,  and  all  this  under  the  assumption  that  the  two  cases 
fall  under  the  former  instead  of  the  latter  relations.  The  facts 
of  order  which  appear  in  the  watch  have  certain  fundamental 
characteristics  utterly  wanting  in  those  which  appear  in  nature, 
and  which  separate  the  two  classes  into  distinct  and  opposite 
species  of  the  general  class,  facts  of  order.  The  fonner,  for  ex- 
ample, possess  essential  characteristics — that  is,  peculiar  combi- 
nations— unlike  any  thing  resulting  from  the  action  of  nature's 
laws.  The  time  was,  for  example,  when  no  such  thing  as  a 
watch,  nor  any  thing  of  the  kind,  had  an  existence.  There  are, 
also,  artificial  combinations  of  a  kind  not  only  unlike  any  thing 
produced  in  nature,  but  which  we  know  can  result  from  the  ac- 
tion of  no  inhering  power  of  nature,  and  therefore,  aside  from 
the  elements  of  order,  supposing  the  action  of  a  designing  power 
out  of  and  above  nature.    These  circumstances  separate  such 


APPLIED     LOGIC.  347 

facts  by  fundamental  specifical  differences  from  facts  of  order 
produced  through  the  action  of  nature's  laws,  and  to  the  pro- 
duction of  which,  from  aught  that  appears  in  the  mere  facts 
themselves,  said  laws  are  adequate.  It  is  only  under  the  prin- 
ciple of  remote  analogy,  in  view,  not  of  their  specifical,  but  ge- 
nerical  elements,  that  we  can  reason  from  one  of  these  classes 
of  facts  to  the  other.  Such,  in  substance,  is  the  reasoning  of 
the  individuals  referred  to,  on  this  subject.  In  our  judgment, 
that  reasoning  has  absolute  validity.  Before  we  can  reason  in- 
ductively from  the  one  class  to  the  other,  we  must  show  that 
they  belong  to  the  same  species,  and  our  reasoning  must  be 
based  wholly  upon  the  specifical  elements  common  to  the  two. 
This  is  done  when  (what  is  not  done  in  the  design  argument  as 
almost  exclusively  presented)  the  order  existing  in  both  alike  is 
shown  to  be  an  effect  originated  in  time,  and  to  possess  other 
common  characteristics  which  render  it  undeniably  evident  that 
neither  any  more  than  the  other,  could  result  from  the  action 
of  laws  inhering  in  nature. 

5.  The  principle  on  which  the  theistic  argument  under  this 
syllogism  has  hitherto  been  conducted  now  claims  our  atten- 
tion. In  our  judgment,  the  conduct  of  this  argument,  we  re- 
peat, is  without  a  parallel  in  the  history  of  science.  In  all  cases, 
where,  in  a  given  syllogism,  one  premise  is  doubted  or  denied 
and  the  other  universally  admitted,  and  where  the  validity  of 
the  latter  is  too  obvious  to  admit  of  doubt  or  denial  in  any 
form,  science  requires  universally  that  the  disputed,  and  not  the 
admitted  premise,  should  be  argued.  In  regard  to  the  theistic 
syllogism  now  before  us,  no  form  of  doubt  or  denial  does  exist, 
or  ever  has  existed,  of  the  validity  of  but  one  of  its  premises — 
the  major.  Yet  in  the  conduct  of  the  argument,  a  few  simple 
illustrations  aside — the  watch,  for  example — the  admitted,  in- 
stead of  the  disputed  premise,  has  been  exclusively  argued. 
Astronomy,  geology,  and  the  sphere  of  all  the  sciences  have 
been  traversed,  to  find  facts  of  order  to  fortify  and  defend  the 
admitted  premise,  and  all  this  while  mountain  ridges  of  facts  of 
this  kind  lay  piled  up,  "  Pelion  upon  Parnassus,"  before  the  uni- 
versal mind— facts,  the  reality  of  which  all  the  world  admit,  to- 


gether  with  the  absolute  and  undeniable  validity  of  the  premise 
whose  validity  they  affirm.  In  the  conduct  of  this  argument, 
the  hostile  forces  have,  in  the  presence  of  all  the  world,  passed 
each  other.  Each  has  assaulted  positions  which  the  other  has 
left  undefended,  and  thrown  up  fortresses  around  positions  which 
the  other  has  not  thought  of  assailing.  The  time  has  now  ar- 
rived when  they  are  called  upon  to  join  issue  on  the  real  point 
in  dispute,  and  that  the  vital  one.  The  time  has  come  espe- 
cially, for  the  advocates  of  theism,  to  find  a  major  which  will  not 
be  disputed,  or  to  place  the  one  which  they  have  selected  be- 
yond dispute  by  demonstrating  its  validity.  This  is  the  exclu- 
sive burden  now  resting  upon  them. 

6.  We  will  now,  in  the  last  place,  give  our  own  estimate  of 
the  real  value  of  the  theistic  argument  as  thus  far  conducted. 
There  are  two  points  of  light  in  which  this  subject  may  be  con- 
templated— the  value  of  the  argument  as  a  means  of  conviction, 
and  as  a  source  of  illustration.  As  a  means  of  conviction,  that 
is,  of  confirming  the  faith  of  actual  believers,  or  of  inducing  con- 
viction in  the  minds  of  unbelievers,  we  regard  the  argument  as 
it  now  stands  as  almost,  if  not  quite,  worthless.  No  facts  ranged 
under  a  general  principle,  for  the  purpose  of  establishing  a  cer- 
tain conclusion,  can  possibly  raise  any  convictions  of  the  truth 
of  said  conclusion  of  a  higher  nature  than  those  already  existing 
in  respect  to  the  validity  of  the  principle  itself.  When  this  ar- 
gument is  addressed  to  the  believer,  it  finds  him  already  more 
immovably  assured  of  the  truth  of  the  conclusion  sought,  to  wit, 
"  God  exists,"  than  he  is  of  the  validity  of  the  principle  pre- 
sented as  the  exclusive  basis  of  the  argument,  to  wit,  "  Facts 
of  order  universally  prove  mind."  The  argument,  then,  can 
have  ho  efficacy  as  a  means  of  confirming  existing  convictions, 
and  if  a  doubt  of  the  validity  of  the  principle  exists,  will  tend 
exclusively  to  weaken  those  convictions.  On  the  other  hand, 
if  the  argument  is  presented  to  one  who  not  only  doubts  the 
conclusion  sought,  but  also  denies  the  validity  of  the  principle 
under  which  our  facts  of  order  are  arranged,  every  fact  of  this 
character  adduced  will  tend  to  but  one  result,  that  is,  to  in- 
crease the  pre-existing  mental  state,  and  that  by  continuously 


APPLIED     LOGIC.  349 

arousing  the  mind  to  a  more  distinct  and  reflective  conscious- 
ness of  the  grounds  of  the  doubt  and  disbelief  referred  to. 
Such,  in  our  judgment,  is  the  value  of  the  argument  before  us 
as  a  means  of  conviction,  the  great  end  for  which  it  has  been 
perfected.  On  the  other  hand,  if  we  would  refer  to  the  various 
productions  embodying  this  argument  as  sources  of  illustration, 
that  is,  as  furnishing  examples  of  the  handiwork  of  an  intelli- 
gent first  cause  already  known  to  exist,  then  such  productions 
as  those  of  Paley  are  invaluable.  As  such,  these  productions 
will  be  resorted  to  long  after  they  have  been  forever  set  aside, 
as  sources  of  valid  proof  of  the  being  of  God. 


INFLUENCE    OF   THE    HYPOTHESIS,    THAT    THERE    ARE    DIFFERENT 
KINDS    OF    PROOF    OF   THE   BEING    OF    GOD. 

Nothing,  in  our  judgment,  has  tended  more  to  obscure  and 
mystify  the  whole  subject  under  consideration,  than  the  suppo- 
sition that  there  are  different  kinds  of  proof  of  the  being  of 
God — such  as  the  d  priori,  the  d  posteriori,  the  cosmological, 
and  teleological.  What,  for  example,  is  the  proper  and  exclu- 
sive sphere  of  d  priori  cognitions  ?  Not  the  real,  as  far  as  sub- 
stances and  causes  are  concerned,  in  any  department  of  thought 
whatever.  A  priori,  we  do  know,  for  example,  that  "  Qualities 
suppose  substances," — "  Events  a  cause,"  and  "  Conditioned  ex- 
istences an  unconditioned  or  ultimate  cause."  A  priori,  we  do 
not  and  cannot  know,  however,  what  kind  of  substances,  causes, 
or  unconditioned  realities  actually  exist,  any  more  than  we  can 
thus  know  what  particular  qualities,  events,  or  conditioned 
realities  actually  exist.  What  would  be  thought  of  a  natural 
philosopher  who  should  profess  to  give  d  priori  demonstrations 
of  the  nature  and  specific  character  of  particular  proximate 
causes  existing  in  the  world  around  us?  Such  a  procedure 
would  be  no  more  absurd  than  an  attempt  at  a  similar  proof  of 
the  being  of  God.  God  is  and  can  be  known  only  as  a  cause — 
the  unconditioned  cause.  We  can  no  more  determine  d  priori 
what  this  cause  is,  than  we  can  thus  determine  the  nature  of 
the  phenomena  of  "  things  that  are  made."     We  can  no  more 


350  LOGIC. 

determine  d  priori  whether  a  world-maker  exists,  than  we  can 
thus  determine  whether  a  watchmaker  exists,  and  that  when 
we  do  not  know  whether  a  world  or  a  watch  exists  (*-  not. 
A  priori  we  cognize  formulas  yielding  certain  specific  deduc- 
tions in  regard  to  the  nature  and  character  of  proximate  causes 
in  the  world  around  us,  and  of  the  unconditioned  cause  of  all, 
and  yielding  said  deductions,  on  the  supposition  that  the  facts 
of  creation  accord  with  those  formulas.  A  posteriori  we  deter- 
mine whether  said  facts  do  or  do  not  accord  with  those  formu- 
las, and  thus  obtain  scientific  deductions  in  regard  to  the  nature 
of  causes  proximate  and  ultimate.  This  is  the  exclusive  pro- 
cedure in  all  the  sciences.  From  the  very  nature  of  the  idea  of 
God,  we  have  and  can  have  no  other  forms  of  valid  proof  of  his 
being  or  perfections.  The  following  may  be  given  as  the  forms 
of  the  only  real  syllogisms  yielding  the  different  elements  of  the 
theistic  deduction,  "  God  exists" : 

First  Syllogism. 
A  priori  premise, 
Facts  of  a  certain  character  affirm  that  the  unconditioned  cause  of  the  order 
existing  in  nature  is  a  power  out  of  and  above  nature  ; 

A  posteriori  premise, 
The  facts  of  the  universe  are  of  this  character  ; 

Conclusion, 
The  unconditioned  cause  of  the  order  existing  in  nature  is  a  power  out  of 
and  above  nature. 

Second  Syllogism. 
A  priori  premise, 
Facts  of  a  certain  character  reveal  this  cause  as  a  self-conscious  personality, 
possessed  of  the  attributes  involved  in  the  ideas  of  infinity  and  perfection. 

A  posteriori  premise, 
Facts  of  creation  of  this  character  do  exist ; 

Conclusion, 
The  unconditioned  is  a  self-conscious  personality,  &o 


APPLIED     LOGIC.  351 

There  is  no  other  possible  form  in  which  we  can  reason  scien- 
tifically from  facts  to  causes  of  any  kind  whatever.  A  priori 
we  determine  what  deductions  must  be  valid,  on  the  supposition 
that  facts  of  a  certain  character  do  exist.  A  posteriori  we  de- 
termine whether  facts  of  that  character  do  or  do  not  exist. 
This  must  hold  in  the  science  of  theology  as  well  as,  and  in  the 
same  form  as,  in  all  other  sciences.  A  priori  we  determine 
nothing  whatever  in  regard  to  the  questions,  whether  real 
causes  do  or  do  not  exist,  and  what  are  the  real  character  of 
causes.  A  posteriori  we  simply  determine  what  facts  do  or 
do  not  exist.  By  the  union  of  the  two  elements  of  thought  be- 
fore us,  we  deduce,  from  principles  and  facts  thus  given,  valid 
conclusions  in  regard  to  the  reality  and  character  of  causes 
proximate  and  ultimate.  To  this  one  form  of  procedure,  sci- 
ence knows  no  exceptions  whatever. 

THE   TWO    ABERDEEN    PRIZE    ESSAYS    DENOMINATED    "CHRISTIAN 
THEISM,"    AND    "  THEISM." 

As  a  further  elucidation  of  the  principles  of  logical  deduction, 
we  have  deemed  it  expedient  to  offer  a  few  criticisms  on  the 
two  works  above  named.  Our  special  object  in  criticising  these 
works  is  the  correction  of  certain  false  systems  of  philosophy — 
systems  which  need  correction  in  order  to  place  philosophy  itself 
on  a  scientific  basis.  From  the  circumstances  of  their  origin, 
we  should  naturally  conclude  that  these  essays  would  embody 
the  theistic  argument  in  the  strongest  forms  in  which  it  now 
exists,  the  prizes  offered  having  been  so  great  (one  of  $9,000 
and  the  other  of  |3,000),  and  the  competitors  so  numerous  (up- 
wards of  two  hundred).  For  ourselves  we  took  up  these  pro- 
ductions with  the  highest  expectations,  and  read  them  with  the 
intensest  interest.  We  laid  them  down  with  the  deep  impres- 
sion, that  if  said  productions  do  present  the  theistic  argument 
in  its  present — and  especially  in  its  present  and  highest  forms — 
then  natural  theology  is  not  only  in  its  infancy,  but  is  yet  in  the 
meshes  of  unsound  and  erfoneous  principles  of  science.  The 
logic  only  of  these  productions  will  be  the  subject  of  criticism. 


"We  will  first  direct  attention  to  the  essay  which  took  the  second 
prize — that  of  Professor  Tulloch. 

Professor  Tulloch'' s  Treatise  {Theism). 

We  have  already  given  the  syllogism  in  conformity  to  which 
the  theistic  argument  is  elaborated  by  our  author,  and  which  is 
given  in  the  first  chapter  of  the  work.  Professor  Tulloch  dis- 
tinctly admits  the  fact,  that  the  major  is  the  only  disputed 
premise  of  the  theistic  syllogism,  as  given  by  himself  and 
others.  Hence,  when  he  comes  to  argue  the  minor,  he  very 
pi'operly  argues  that  under  the  title,  "Illustrative  (inductive) 
evidence."  The  only  real  question  at  issue,  he  asserts,  pertains 
exclusively  to  the  claims  of  the  major  premise.  In  respect  to 
it — to  wit,  that  "  Order  universally  proves  mind," — he  says, 
"Upon  this  fundamental  position  rests  the  whole  burden  of  the 
theistic  argument."  Again,  he  adds,  speaking  of  the  same 
premise,  "  There,  accordingly,  the  whole  contest  of  theism  cen- 
tres, and  finds  its  most  vital  struggle.  And  of  this  the  opposite 
school  of  thinkers  are  sufficiently  aware.  They  clearly  feel  that 
it  is  here  alone  that  a  consistent  position  of  denial  can  be  taken 
up."  We  were  not  mistaken,  then,  when  we  asserted  that  the 
theistic  syllogism,  as  presented  by  our  author  and  others,  has  a 
disputed  major  and  a  universally  admitted  minor.  Nor  will  it 
be  doubted  that  previously  to  the  appearance  of  Professor  Tul- 
loch's  work,  the  admitted  instead  of  the  disputed  premise  had 
been  almost  exclusively  argued  by  theistic  writers. 

In  what  position  does  this  representation  place  the  science  of 
theology  ?  It  has  within  its  own  proper  sphere,  if  this  repre- 
sentation is  true,  no  ultimate  principles  or  "  first  truths."  It  is 
altogether  a  secondary  science,  its  highest  principle — the  major 
premise,  in  itself  a  problematical  judgment — being  the  conclu- 
sion of  a  prosyllogism,  whose  validity  is  to  be  determined  exclu- 
sively within  the  sphere  of  another  and  totally  different  science. 
For  ourselves,  we  do  not  believe  that  the  eternal  truth  which 
lies  at  the  foundation  of  all  religion ,'  has  such  a  basis.  The  sci- 
ence of  theology,  we  believe,  rests  upon  ultimate  principles  lying 


APPLIED     LOGIC.  353 

within  its  own  appropriate  sphere,  and  which  must  and  will, 
when  rightly  presented,  be  universally  admitted  to  be  strictly 
analytical  judgments — that  is,  universal  and  necessary  intuitive 
truths.  "  The  whole  contest  of  theism,"  on  the  other  hand, 
must,  when  the  science  is  properly  developed,  centre  and  "  find 
its  most  vital  struggle,"  not  in  reference  to  the  first  principle  of 
the  science — the  major  premise — but  in  regard  to  matters  of 
fact,  that  is,  the  minor  premise.  It  is  a  reversal  of  all  the  laws 
and  principles  of  scientific  procedure  to  suppose  the  opposite. 

In  resting  the  whole  science  of  theology,  therefore,  upon  a 
mere  problematical  judgment,  it  became  the  author  to  place  the 
question  of  the  validity  of  that  judgment  beyond  dispute,  by  an 
unanswerable  demonstration  of  its  truth.  Otherwise  the  funda- 
mental doctrine  of  all  religion  is  made  to  rest  upon  an  uncer- 
tain basis.  The  question  which  now  arises,  the  question  upon 
which  the  entire  logical  claims  of  his  whole  work  must  rest, 
is,  Has  he  done  this  ?  Has  he  demonstrated  the  truth  of  his 
major  premise,  "  Order  universally  proves  mind  ?"  To  a  con- 
sideration of  this  one  question  we  will  now  advance.  After 
some  explanatory  statements  and  remarks  in  the  first  chapter, 
this  question  is  argued  at  length  in  chapter  second,  and  the  en- 
tire superstructure  subsequently  reared  must  stand  or  fall  with 
the  validity  of  the  argument  in  this  single  chapter ;  for  here 
alone  he  argues  what  he  himself  affirms  to  be  the  "  vital  ques- 
tion"— the  major  premise.  Let  us,  then,  examine  the  argu- 
ment as  here  developed. 


Professor  TullocJi's  professed  Demonstration  of  Ms  Major 
Premise. 

On  a  careful  examination  of  what  appears  in  this  chapter,  it 
will  be  seen  at  once  that  the  learned  author  does  not  argue  this 
question  directly  and  immediately  at  all,  but  another  and  dif- 
ferent question ;  one,  however,  which,  as  he  affirms,  directly 
and  immediately  implies  this.  The  proposition  which  he  at- 
tempts to  establish  is  not  this  :  "  Order  universally  proves 
mind,"  but  this :  Any  event,  whatever  it  may  be,  proves  mind. 


354  LOGIC. 

If  the  latter  proposition  is  established,  the  former,  par  emi- 
nence, he  concludes,  and  rightly  too,  is  established.  That  we 
may  not,  even  in  appearance,  misrepresent  our  author,  we 
will  present  the  following  somewhat  lengthy  extract  from  the  ' 
first  chapter — an  extract  in  which  he  distinctly  defines  his  own 
position : 

"  In  endeavoring  to  verify  the  position  which  forms  the  argu- 
mentative basis  of  our  evidence,  there  are  two  special  lines  of 
proof  demanded  of  us — the  one  relating  directly  to  the  position 
itself,  that  '  Order  universally  proves  mind,'  or,  in  other  words, 
that  '  Design  is  a  principle  pervading  the  universe ;'  and  the 
other  relating  to  a  doctrine  which,  as  it  appears  to  us,  lies  every- 
where involved  in  the  more  special  theological  principle.  This 
principle,  in  the  form  announced  in  our  first  proposition,  un- 
doubtedly implies  a  definite  doctrine  of  causation.  In  asserting 
the  principle  of  design,  we  clearly  assert  at  the  same  time,  that 
mind  alone  answers  to  the  true,  or  at  least  ultimate,  idea  of 
cause.  We  pronounce  causation,  or  at  least  our  highest  con- 
ception of  it,  to  imply  efficiency.  But  does  it  really  do  so  ? 
We  find  ourselves  met  on  this  general  philosophical  ground  as 
to  the  true  nature  of  causation,  as  well  as  on  the  ground  of  the 
special  theological  application  which  we  make  of  the  general 
truth.  They  who  dispute  the  theistic  interpretation  of  nature, 
no  less  dispute  the  doctrine  of  efficient  causation,  and  in  fact 
base  their  opposition  to  the  highest  principle  on  this  lower  and 
wider  ground. 

"  In  order,  therefore,  fully  to  sustain  our  position,  we  must 
make  it  good  on  this  lower  ground.  According  to  our  whole 
view,  the  one  position  is  untenable  apart  from  the  other." 

Here,  it  will  be  seen,  that  our  author  not  only  affirms,  as  the 
doctrine  which  he  is  to  establish,  that  mind  is  the  only  existing 
real  or  efficient  cause,  but  that  to  prove  the  higher  proposition, 
*'  Order  universally  proves  mind,"  he  must  prove  the  lower 
one,  Any  event  proves  mind.  Further  on,  this  last  proposition 
takes  a  still  different  form,  to  wit,  Any  event  proves  a  rational . 
will — the  doctrine  of  the  essay  being  this,  that  will  is  the  only 
existing  real'cause  of  any  event  whatever.     "A  cause,"  he  says, 


APPLIED     LOGIC.  355 

"  we  have  found  to  be  truly  coincident  with  an  agent ;  to  have 
its  primitive  type  in  the  ego,  the  living  root  of  our  being  ;  and 
to  be  especially  represented  in  that  which  constitutes  the  highest 
expression  of  our  being — free  will.  A  cause,  therefore,  implies 
mind.  More  definitely,  and  in  its  full  conception,  it  implies  a 
rational  will."  This  is  the  only  proposition  bearing  upon  the 
subject  that  he  even  attempts  to  establish  in  this  chapter.  The 
theistic  syllogism  as  argued  by  him  is  really  and  truly  this : 
First  or  major  premise, 

Any  event  whatever  proves  a  rational  will ; 
Second  or  minor  premise, 

The  works  of  nature  discover  events  ; 
Conclusion, 

The  works  of  nature  prove  a  rational  will. 

Upon  the  validity  of  the  major  premise  of  this  syllogism,  or 
rather  upon  our  author's  professed  demonstration  of  its  validity, 
the  claims  of  the  fundamental  doctrine  of  all  religion  is  wholly 
based  in  this  treatise,  and  all  who  accept  the  treatise  as  proper- 
ly and  adequately  representing  the  theistic  argument,  must  ac- 
cept of  the  doctrine  of  the  being  of  God  as  having  a  foundation 
no  more  solid  and  immovable.  Let  us  now  advance  to  a  direct 
consideration  of  our  author's  professed  demonstration  of  the 
proposition  before  us. 

Our  Author's  Indirect  and  Preliminary  Argument. 

In  his  indirect  and  preliminary  argument,  in  which  he  com- 
bats the  doctrine  of  causation  as  maintained  by  Messrs.  Hume, 
Brown,  Mill,  and  others — to  wit,  that  cause  is  nothing  but  "  an- 
tecedence immediate  and  invariable," — our  author  is  undeniably 
triumphant.  All  that  we  perceive  relatively  to  the  facts  of  the 
universe^  these  authors  maintain,  is  simply  succession  of  events, 
and  nothing  else.  From  this  fact,  which  is  undeniable,  and 
equally  so  in  respect  to  mental  and  physical  facts,  they  assume 
that  no  other  relation  than  that  of  mere  antecedence  and  conse- 
quence exists  between  successive  events.     There  is  no  correla- 


356  LOGIC. 

tion  between  the  antecedent  and  consequent  which  makes  it 
necessary  that  one  particular  consequent  instead  of  another,  or 
none  at  all,  should  be  connected  with  any  particular  antecedent. 
Take  away  all  antecedents  of  every  kind,  and  as  far  as  the  na- 
ture of  things  is  concerned,  precisely  the  same  consequents  as 
now  appear  are  just  as  possible  and  as  likely  to  arise,  as  when 
these  antecedents  are  given.  To  this  view  of  the  doctrine  of 
causation  our  author  replies  in  the  following  language  : 

"  When  on  the  appearance  of  any  change  we  instinctively 
pronounce  it  to  have  a  cause,  what  do  we  really  mean  ?  Do 
we  affirm  merely  that  some  other  thing  has  gone  before  the  ob- 
served phenomenon  ?  Is  priority  the  constitutive  element  of 
our  intellectual  judgment  ?  Is  it  not  rather  something  quite 
different  ?  Is  not  our  judgment  characteristically  to  this  effect 
— that  some  other  thing  has  not  only  preceded,  but  produced 
the .  change  we  contemplate  ?  Nay,  is  it  not  this  idea  of  pro- 
duction that  we  particularly  mean  to  express  in  the  use  of  the 
term  '  cause  ?'  Succession  is  no  doubt  also  involved,  but  it  is 
not  the  relation  of  succession  with  which  the  mind  in  the  sup- 
posed judgment  is  directly  and  initially  concerned,  but  rather 
the  relation  of  power.  That  when  we  speak  of  cause  and  effect, 
we  express  merely  the  relation  of  conjunction  between  phe- 
nomena of  antecedence  and  consequence  in  any  defined  sense, 
is  something  of  which  no  ingenuity  of  sophistry  will  ever  be 
able  to  persuade  the  common  mind.  It  matters  not  in  the  least 
degree  that  it  can  be  so  clearly  proved  that  nothing  intervenes 
between  the  simple  facts  observed,  that  we  see  in  the  sequence 
of  the  phenomena.  This  is  not  in  dispute.  Only  the  intel- 
lectual common  sense  insists  on  recognizing  a  deeper  relation 
among  phenomena  than  mere  sequence.  It  accepts  the  order 
of  succession,  which  is  the  special  function  of  science  to  trace 
everywhere  to  its  most  general  expression  ;  but  it  moreover 
says  of  this  order,  that  it  is  throughout  produced,  or,  in  other 
words,  that  it  is  only  explicable  as  involving  a  further  element 
of  power.  That  it  is  really  the  import  of  the  intellectual  judg- 
ment which  we  pronounce  in  speaking  of  cause  and  effect — to 
which  the  very  words  themselves  testify  in  an  unmistakable 


APPLIED     LOGIC.  357 

manner — is  so  clear,  that  it  is  now  admitted  by  every  school  of 
philosophy  which  does  not  rest  on  a  basis  of  materialism,  and 
has  even  been  conceded  by  writers  of  this  school,  however  irre- 
solvable on  their  principles." 

No  individual,  we  are  bold  to  affirm,  can  by  any  possibility 
refute  the  above  argument,  or  show  that  it  is  not  perfectly  fatal 
to  the  theory  of  causation  to  which  said  argument  stands  op- 
posed. The  advocates  of  this  theory  overlook  wholly  a  fundar 
mental  fact  of  universal  consciousness,  the  absolute  affirmation 
that  there  are  in  the  human  mind  two  distinct  forms  of  know- 
ledge equally  valid — a  knowledge  of  what  we  directly  and  im- 
mediately perceive  to  be  true,  and  a  knowledge  of  what  is 
necessarily  implied  in  what  we  perceive.  We  know  that  body 
exists,  because  we  have  a  presentative  knowledge  of  it  as  ac- 
tually existing.  In  knowing  that  body  does  exist,  we  know 
that  space  must  exist,  although  it  is  not  an  object  of  immediate 
perception,  the  reality  of  space  being  necessarily  implied  in  that 
of  body.  So  in  cognizing  succession  and  phenomena  as  reali- 
ties, we  know  that  time  and  substances  must  be  realities  also. 
As  body  necessarily  supposes  space,  succession  time,  and  phe- 
nomena substance,  in  knowing  by  immediate  perception  the 
first  class  of  objects  as  real,  we  know  with  equal  absoluteness 
that  the  latter  class  must  be  realities  also.  The  same  principles 
apply  to  our  knowledge  of  causation.  In  knowing  that  any 
event  whatever  has  occurred,  we  know  absolutely,  as  necessarily 
implied  in  the  occurrence  of  said  event,  not  only  that  it  had  an 
antecedent,  but  a  real  efficient  determining  cause.  We  know 
that  this  must  be  true,  because  we  cannot  even  conceive  the  op- 
posite as  being  true.     We  will  now  consider, 

Our  Author's  Direct  and  Positive  Argument. 

In  demonstrating  the  fact  that  the  theory  of  causation  main- 
tained by  Mr.  Hume,  Mill,  and  others,  is  not  true,  we  have  de- 
termined the  truth  of  the  doctrine  that  there  are  real  determin- 
ing efficient  causes — causes  which  are  the  true  and  proper  ante- 
cedents of  all  events.     We  have  by  this  means,  however,  deter- 


858  LOGIC. 

mined  nothing  in  regard  to. the  nature  or  location  of  said  causes, 
whether,  for  example,  they  are  exclusively  physical  or  mental, 
or  whether  there  are  in  reality  both  mental  and  physical  causes. 
According  to  our  author,  all  real  causation  is  exclusively  men- 
tal. "According  to  this  whole  view,"  he  says,  "there  is  no 
such  thing  as  mere  physical  causation."  Again,  "Physical 
causes,  apart  from  the  idea  of  a  will  in  which  they  originate 
and  which  they  manifest,  have  no  meaning." 

How,  permit  us  to  ask  in  the  first  place,  can  the  truth  of  such 
a  doctrine — supposing  it  true — he  established  ?  Not  surely  d 
priori.  We  cannot  thus  determine  whether  matter,  on  the  one 
hand,  or  mind,  on  the  other,  is  or  is  not  the  real  and  proper 
cause  of  certain  effects.  For  aught  that  we  can  thus  determine, 
there  may  be  real  physical  causes  of  physical  effects,  and  also  of 
mental  phenomena,  as  well  as  mental  causes  of  mental,  on  the 
one  hand,  and  of  physical  effects,  on  the  other.  A  priori  we 
cannot  affirm,  that  matter  as  well  as  mind  is  not. a  real  and 
proper  power  in  regard  to  certain  events.  This  is  undeniable. 
It  is  wholly  d  posteriori,  that  is,  by  a  knowledge  of  facts  mental 
and  physical,  that  this  doctrine,  if  true  and  if  its  truth  is  ascer- 
tainable, can  be  established. 

It  is  further  evident,  and  undeniably  so,  that  this  doctrine  if 
true  cannot  be  proven  by  any  reference  to  what  is  intrinsic  in 
any  mental  or  physical  facts  contemplated  by  themselves,  or 
when  compared  with  one  another.  Take  any  act  of  will,  for 
example,  we  please,  and  from  what  is  intrinsic  in  the  act  itself, 
or  by  comparing  it  with  any  mental  or  physical  fact,  we  cannot 
determine  that  such  act  is  a  cause  proper  of  such  fact,  much 
less  that  acts  of  will  are  the  only  real  causes  of  other  mental 
and  of  all  physical  events.  It  is  by  no  inspection  or  dissection 
of  mental  and  physical  facts  that  this  doctrine,  if  susceptible  of 
proof,  can  be  proven.  If  susceptible  of  proof  at  all,  it  must  un- 
deniably be  through  some  relation  of  these  tacts  to  one  another 
— a  relation  given  in  consciousness. 

We  are  now  prepared  to  take  up  the  question,  By  what  means 
does  our  author  attempt  to  prove  his  own  doctrine  ?  Simply 
and  exclusively,  we  answer,  by  an  attempted  proof  of  the  psy« 


APPLIED     LOGIC.  359 

chological  proposition,  that  it  is  exclusively  through  the  con- 
sciousness of  our  acts  of  will  as  causes  that  we  originally  ob- 
tained our  idea  of  causation.  From  this  one  source  exclusively, 
he  affirms,  was  our  idea  of  causation  originated.  On  this  one 
assumed  fact,  the  universal  assumption  is  based  that  a  rational 
will  is  the  only  real  existing  efficient  cause.  "  The  question  be- 
fore us,  then,"  he  affirms,  "  really  passes  into  the  old  one  as  to 
the  origin  of  our  knowledge."  To  prove  that  this  idea  was  not 
originally  given  by  external  material  facts,  and  that  it  Avas  given 
by  the  consciousness  of  mental  acts — acts  of  will — he  makes  the 
following  statements  :  "  That  this  idea"  (that  of  causation)  "  is 
not  derived  from  without — that  it  does  not  come  through  any 
phase  of  sensational  experience — is  already  clear  in  the  fact  ad- 
mitted on  all  hands,  that  we  only  perceive  succession^-that  we 
are  only  conversant  through  the  senses  with  the  two  terms  of  a 
sequence.  But  if  not  from  without  it  must  be  from  within  ;  we 
must  have  the  idea  of  power  given  us  in  our  own  mental  expe- 
rience." Again  :  "  With  the  dawn  of  mind  we  apprehend  our- 
selves as  distinct  from  the  objective  phenomena  surrounding  us ; 
the  ego  emerges,  face  to  face,  with  the  non-ego.  And  in  this 
springing  forth  of  self,  so  far  back  in  the  mental  history  as  to 
elude  all  trace,  is  primarily  given  the  idea  of  power. 

"  What  is  commonly  called  the  will,  therefore,  is,  according 
to  this  view,  the  ultimate  source  or  fountain  of  the  notion  of 
power." 

In  thus  determining,  as  our  author  supposes  he  has  done,  the 
source  from  whence  the  idea  of  power  or  cause  was  originally 
derived,  he  assumes  that  he  has  also  determined  the  exclusive 
source  of  causation  itself,  that  is,  that  he  has  demonstrated  that 
"  rational  will"  is  the  only  real  existing  cause.  In  other  words, 
in  proving  that  we  originally  derived  our  idea  of  cause  from  the 
consciousness  of  mental  acts,  we  have  demonstrated  the  fact, 
that  a  "  rational  will"  not  only  is  a  cause  of  some  facts,  but  the 
exclusive  cause  of  all  facts  whatever — that  matter,  consequently, 
is  not  the  cause"  of  any  events  whatever.  Such  is  the  argument 
of  our  author.     In  regard  to  it  we  remark  : 

1.  That  granting  our  author's  theory  of  the  origin  of  our  idea 


360  LOGIC. 

of  causation  to  be  true,  the  inference  that  he  deduces  from  it 
presents  one  of  the  most  palpable  and  singular  leaps  in  logic 
that  Ave  ever  met  with.  The  fact  professedly  ascertained  is 
this  :  In  the  consciousness  of  mental  acts  we  originally  obtained 
our  idea  of  causation.  The  conclusion  deduced  from  this  as- 
sumed fact  is  this  :  "  There  is  no  such  thing  as  mere  physical 
causation."  In  other  words,  facts  of  mind  originate  the  idea  of 
causation  in  the  mind  itself.  Matter,  therefore,  is  the  real  cause 
of  no  facts  whatever.  What  conceivable  connection  is  there 
between  such  a  fact,  granting  it  real,  and  such  a  conclusion  as 
that  ?  How  do  we,  how  can  we  know,  that  that  which  origi- 
nates the  idea  of  cause  in  our  minds  is  itself  the  only  source  of 
real  causation  ?  Matter,  for  aught  we  know  or  can  know,  may 
be  the  real  cause  of  certain  facts,  and  yet  we  have  derived  our 
idea  of  cause,  not  from  matter  but  from  facts  of  mind.  This  is 
undeniable. 

2.  By  no  possibility  can  the  validity  of  this  theory  of  the  ori- 
gin of  our  idea  of  causation  be  verified.  We  have  no  remem- 
brance of  the  source  from  whence  this  idea  was  derived.  Nor 
can  we  legitimately  affirm  that  because,  as  far  as  physical  phe- 
nomena are  concerned,  we  perceive  nothing  but  succession,  we 
did  not  from  hence  derive  our  original  idea  of  causation.  In 
our  present  consciousness,  in  cases  where  we  perceive  nothing 
but  succession,  the  idea  of  any  event  whatever  is,  by  a  necessi- 
ty of  our  intellectual  constitution,  connected  with  the  idea  of 
cause.  For  aught  that  we  can  know,  this  idea  by  the  same  ne- 
cessity did,  in  fact,  connect  itself  with  the  very  first  event  which 
we  did  perceive,  whether  it  was  mental  or  physical.  We  know 
that  it  is  a  fixed  law  of  our  intellectual  constitution,  that  when 
any  fact  whatever  is  perceived,  with  the  conception  of  that  fact 
is  originated  also  its  logical  antecedent.  Thus  with  the  concep- 
tion of  body,  which  we  perceive,  is  originated  the  conception  of 
space,  which  we  do  not  perceive.  Thus  also  the  perception  of 
succession  originates  the  idea  of  time,  and  the  perception  of 
phenomena  that  of  substance.  Now  the  same  law  which  origi- 
nates the  ideas  of  space,  time,  and  substance,  on  the  perception 
of  body,  succession,  and  phenomena,  must  originate  that  of 


APPLIED     LOGIC.  361 

cause,  on  the  perception  of  any  event  whatever,  whether  men- 
tal or  physical.  Unless  it  can  be  shown,  therefore, — and  it  can- 
not be — that  acts  of  will  were,  in  fact,  the  first  objects  of  per- 
ception, it  cannot  be  shown  that  we  did  derive  from  them  our 
idea  of  cause.  In  that  case,  also,  that  origin  would  be  merely 
accidental,  any  other  event  being  equally  adequate  to  the  origi- 
nation of  the  idea. 

3.  By  the  same  argument — granting  its  validity — by  which 
our  author  would  prove  that  we  could  not  have  derived  our 
idea  of  cause  from  external,  we  will  prove  that  we  could  not 
have  derived  it  from  internal,  phenomena.  We  could  not  have 
derived  it,  he  argues,  from  the  former,  because  here  we  perceive 
only  succession.  It  is  equally  and  undeniably  true  that  in  the 
consciousness  of  internal  facts,  we  perceive  nothing  but  succes- 
sion. We  have  the  consciousness  of  one  mental  act  or  state, 
and  then  of  another.  So  also  of  all  mental  states  and  their 
physical  consequents.  Nothing  but  succession  of  phenomena 
can,  by  any  possibility,  be  an  object  of  perception,  external  or 
internal.  The  idea  of  causation  is  exclusively  an  idea  of  reason 
— an  idea  given,  like  those  of  space,  time,  and  substance,  on 
occasion  of  perception,  but  not  in  perception  itself,  external  or 
internal.  If  these  external  facts,  because  we  find  in  them  only 
succession,  cannot  give  this  idea,  for  the  same  reason  internal 
facts  cannot  give  it,  for  here  also  perception  gives  only  succes- 
sion. From  the  nature  of  the  idea,  however,  each  class  of  per- 
ceptions is  equally  capable  of  originating  the  idea  ;  and  which, 
in  fact,  does  originate  it  in  the  experience  of  any  one  individual, 
we  have  no  means  of  determining. 

4.  We  have  all  the  evidence  that  matter  is  the  cause  proper 
of  certain  physical  facts  and  mental  states,  on  the  one  hand, 
that  we  have  or  can  have,  in  our  present  state  of  knowledge, 
that  mind  is  the  cause  proper  of  certain  mental  and  physical 
facts,  on  the  other.  As  far  as  we  can  perceive,  certain  physical 
causes  are  as  necessarily  connected,  and  that  in  the  relation  of 
real  causation,  with  certain  physical  facts,  as  mind  is  with  any 
mental  facts.  Let  us  now  contemplate  the  proposition,  that  we 
have  the  same  evidence  that  material  substances  are  the  causes 


362  LOGIC. 

proper  of  mental  states,  that  we  have  that  mind  or  will  is  the 
cause  proper  of  physical  facts.  When  "  for  the"  first  time  the 
ego  emerges,  face  to  face,  with  the  non-ego?  what  relation 
does  the  former  then  recognize  itself  as  sustaining  to  the  lat- 
ter ?  Is  it  this,  that  the  former  as  "  a  rational  will,"  is  the  ex- 
clusive cause  of  all  effects,  and  that  the  latter  is,  in  no  proper 
sense,  a  real  power,  in  no  real  sense  the  cause  proper  of  any 
effects  whatever — effects  mental  or  physical  ?  By  no  means. 
Prior  to  all  acts  of  will  of  any  kind,  mind  finds  itself  to  have 
been  the  subject  of  the  action  of  causes  whose  action  produced 
fundamental  mental  states,  and  that  antecedent  to  and  wholly 
independent  of  all  forms  of  voluntary  activity  on  its  part.  Sen- 
sation, perception,  and  the  consequent  consciousness  of  the  same, 
precede  all  acts  of  will,  and  as  antecedents  lead  to  the  same. 
In  the  consciousness  of  sensation  particularly,  mind — the  ego — 
is  not  revealed  to  itself  as  a  cause  at  all,  but  exclusively  as  the 
subject  of  the  action  of  causes  wholly  ab  extra.  Now  it  is  un- 
deniable, that  the  mind  has  and  can  have  no  higher  evidence 
that  it  is  the  cause  proper  of  any  physical  facts  whatever,  than 
it  has  that  the  non-ego  which  it  thus  beholds  "  face  to  face,"  is 
the  cause  proper  of  sensation.  We  have  all  the  evidence  that 
the  non-ego,  as  a  real  cause,  induces  primal  mental  states,  that 
we  have  or  can  have  that  mind,  in  its  subsequent  voluntary  ac- 
tivity, is  the  real  cause  of  any. changes  whatever  in  external  na- 
ture. There  is  just  as  much  evidence  of  the  truth  of  the  dogma, 
that  matter  is  the  exclusive  efficient  cause  of  all  effects,  and  that 
there  is  no  such  thing  as  mental  causation,  as  there  is  that  mind 
or  will  is  the  only  real  cause,  and  that  there  is  no  such  thing  as 
mere  physical  causation ;  and  there  is  and  can  be  absolutely  no 
evidence  whatever,  in  our  present  state  of  knowledge,  of  the 
truth  of  either  dogma.  The  evidence  that  matter,  on  the  one 
hand,  and  mind,  on  the  other,^re  each  alike  causes  proper,  is, 
in  our  conscious  experience,  perfectly  balanced.  We  have  pre- 
cisely, we  repeat,  the  same  evidence  that  the  non-ego  really 
produces  changes  in  and  limits  the  activity  of  the  ego,  that  we 
have  or  can  have  that  the  latter  produces  any  changes  in  the 
former.    The  most  that  can  in  any  case  be  said  of  the  theory  of 


APPLIED     LOGIC.  363 

our  author  is,  that  it  possibly  may  be  true  in  fact.  Of  its  truth, 
however,  if  true,  we  have  and  can  have — without  a  revelation 
from  God — no  positive  evidence  in  any  form  whatever. 

5.  That  will,  we  remark  finally,  is  not  the  only  efficient  cause, 
we  have  well-nigh,  if  not  quite,  demonstrative  proof.  In  the 
order  of  nature  in  the  infinite  and  eternal  mind,  the  action  of 
intelligence  precedes  that  of  the  will.  This  is  undeniable.  In 
the  finite  mind,  too,  states  of  the  sensibility  and  intelligence 
were  originally  induced  by  causes  wholly  db  extra,  prior  to 
all  foi  ms  of  voluntary  activity,  and  we  have  now  in  conscious- 
ness continuous  experiences  of  precisely  similar  results.  What 
higher  evidence  can  we  have  of  any  fact  than  we  have  here  of 
the  truth  of  the  doctrine,  that  the  will  is  not  the  only  form  and 
source  of  efficient  causation  ?  We  have,  then,  not  only  no  evi- 
dence whatever  of  the  truth  of  our  author's  theory  of  causation, 
but  nearly,  if  not  quite,  demonstrative  proof  that  it  is  not  and 
cannot  be  true. 

What  then  is  the  bearing  of  such  a  conclusion  upon  the 
merits  of  the  work  before  us,  upon  its  merits  in  a  logical  point 
of  view  ?  Nothing  but  this  :  As  an  argument  for  the  being  of 
God  the  work  is  a  total  failure.  The  author  has  himself  formal- 
ly committed  the  logical  claims  of  the  whole  argument  through- 
out to  the  validity  of  one  principle — his  theory  of  causation. 
That  theory  failing  of  valid  evidence,  as  it  undeniably  does, 
the  whole  argument  as  developed  in  the  work  visibly  appears 
resting  upon  nothing  but  a  bank  of  sand. 

But  this  work  is  not  only  logically  inconclusive,  but  equally 
self-contradictory.  After  spending  upwards  of  three  hundred 
pages  in  elaborating  the  theistic  syllogism,  as  presented  in  chap- 
ter first  and  already  considered  by  us — in  Sect.  3,  Chapter.  IV., 
he  formally  abandons  his  previous  argument  as  inconclusive, 
and  affirms  that  the  real  proof*  of  the  divine  existence  is  intui- 
tive or  a  priori.  In  treating  of  the  divine  infinity  in  this  chap- 
ter, he  falls  back  from  "  the  theistic  syllogism"  altogether,  and 
rests  the  whole"  question  of  the  divine  existence  itself  exclusive- 
ly upon  intuition.  By  one  form  of  intuition  (the  lower)  we 
attain  to  a  direct  and  immediate  knowledge  of  the  finite  as  real. 


364  LOGIC. 

By  another  and  higher  form  of  intuition  we  similarly  attain  to 
a  similar  knowledge  of  the  infinite.  "  The  infinite,"  he  says, 
"  is  the  peculiar  object  of  this  higher  intuition.  It"  (the  infi- 
nite) "  is  the  revelation  of  reason,  as  the  finite  is  the  revelation 
of  sense." — "  The  infinite,"  he  says  again,  "  is  apprehended  by 
us  in  the  strongest  manner,  but  then  the  evidence  of  this  reali- 
ty is  directly  found  in  the  intuitive  apprehension  of  the  ego?'' 
If  "  the  evidence"  of  the  divine  existence  is  found  here — and 
our  author  now  affirms  that  it  is — it  is  not,  of  course,  to  be 
found  in  any  of  his  previous  presentations.  According  to  the 
express  teaching  of  inspiration,  however,  "  the  eternal  power 
and  Godhead"  of  deity,  are,  in  fact,  "  clearly  seen,  being  under- 
stood," not  by  immediate  intuition,  but  "  by  the  things  that 
are  made."  We  have,  also,  as  we  judge,  already  sufficiently 
proven  the  fact,  that  there  is  no  such  d  priori  proof  or  know- 
ledge of  God,  or  of  any  other  power  or  cause  in  existence.  For 
this  one  form  of  proof,  however,  our  author  formally  abandons 
all  others.  "  The  infinite,"  he  says,  "  no  longer  regarded  as  a 
mere  subjective  reflection  in  the  understanding — a  mere  logical 
necessity — but  as  intuitively  given  in  reason,  needs  and  admits 
of  no  other  proof  of  reality  than  its  being  thus  given."  Again : 
"  And  in  thus  abandoning  all  claim  to  demonstration,  the  evi- 
dence of  the  being  of  God,  so  far  from  being  weakened,  is  in- 
deed strengthened.  For  in  all  our  knowledge  there  is  and  can 
be  no  higher  warrant  for  reality  than  the  grasp  of  intuition." 

Has  this  learned  author  spent  three  hundred  pages  in  elabo- 
rating what  he  calls  "  the  thelstic  syllogism,"  for  the  purpose  of 
thus  exposing  its  utter  invalidity,  and  of  showing  that  the  case 
"needs  and  admits"  of  no  such  form  of  proof ?  This  must 
have  been  the  case  if  he  understood  himself. 

* 

MR.   THOMSON'S   TREATISE    (CHRISTIAN  THEISM). 

The  theistic  argument,  as  developed  by  Mr.  Thomson,  rests 
upon  the  same  principle,  and  is  elaborated,  as  far  as  the  ques- 
tion relative  to  the  being  of  God  is  argued  at  all  in  his  treatise, 
in  conformity  to  the  6ame  syllogism  as  that  of  Professor  Tnl- 


APPLIED     LOGIC.  365 

loch,  to  wit,  the  argument  from  design.  "  It  is  the  argument 
of  natural  theology,"  says  Mr.  Thomson,  "that  design  must  im- 
ply a  designer,  and  that  which  designs  is  mind."  Again,  in  an- 
swer to  the  question,  "Is  the  First  Cause  a  living  God  ?"  he 
says,  "  The  answer  to  this  question  depends  chiefly  on  the  argu- 
ment from  design.  The  cosmological  argument  gives  us  a  First 
Cause  of  all  things,  an  origin  of  all  the  latent  causes  of  living 
mind,  but  it  cannot  assure  us  that  he  is  himself  mind  or  spirit, 
till  we  have  observed  what  are  the  particular  powers  and  prop- 
erties of  this  living  mind,  and  what  are  the  particular  forms  and 
adaptations  of  exteraal  nature."  But  while  the  syllogisms  of 
the  two  treatises,  though  perhaps  somewhat  different  in  form, 
are  really  and  truly  identical  in  substance,  there  are,  among 
others,  the  following  fundamental  differences  between  them  as 
far  as  the  conduct  of  the  argument  is  concerned : 

1.  While  Professor  Tulloch,  in  the  commencement  of  his 
work,  lays  out  his  whole  strength  in  an  attempted  demonstra- 
tion of  the  validity  of  his  major  premise,  Mr.  Thomson  spends 
nearly,  if  not  quite,  the  first  third  of  his  treatise  in  the  work  of 
invalidating  the  minor  premise  in  his  syllogism,  and  that  while 
he  substitutes  no  other  premise  in  its  place. 

2.  The  entire  production  of  the  former  proceeds  upon  the 
assumption,  that  our  knowledge  of  the  facts  from  which  he  rea- 
sons is  valid — objectively  so — and  hence  that  the  deductions 
which  they  yield  have  a  corresponding  validity.  That  of  the 
latter  proceeds  upon  the  assumption,  that  all  our  assumed 
knowledge,  external  and  internal,  is  only  phenomenal,  and  has 
no  objective,  but  merely  a  subjective  validity ;  and  that  when 
we  reason  from  the  objects  of  said  knowledge  to  God,  we  rea- 
son only  from  the  really  unknown  to  the  still  more  profoundly 
unknown. 

3.  The  principles  and  deductions  of  the  former  are  through- 
out evangelical.  The  fundamental  principles,  together  with 
their  entire  logical  consequences  of  the  latter,  are  in  a  corre- 
sponding degree  skeptical,  and  tend  exclusively  to  confirm  the 
doubts  or  disbelief  of  the  skeptic,  and  utterly  to  unsettle  the 
faith  of  the  theist.     We  speak  only  of  the  principles  of  the 


work,  and  of  the  logical  consequences  of  the  same,  and  not  at 
all  of  the  intentions  of  the  author.  We  will  now  proceed  to 
verify  all  these  statements  in  respect  to  the  work  before  us. 

On  what  condition  can  any  deductions  from  the  facts  of  na- 
ture, mental  and  physical,  as  given  in  our  intelligence,  have 
logical  validity  in  regard  to  God  as  the  first  cause  of  said  facts  ? 
On  one  condition  exclusively,  that  our  knowledge  of  said  facts 
has  objective  as  well  as  subjective  validity ;  in  other  words,  that 
our  knowledge  pertains  to  realities  as  they  are.  Otherwise  we 
do  not  and  cannot  know,  that  we  are  in  the  presence  of  any 
real  indications  of  design  or  not.  Suppose  that  we  have  had 
dreams,  and  know  them  to  be  such — dreams  yielding  visions 
corresponding  throughout  to  all  forms  of  our  present  know- 
ledge of  the  universe.  Would  not  the  world  justly  affirm  that 
we  were  logically  dreaming,  if  we  should  under  the  principle, 
that  "  design  supposes  a  designer,"  reason  from  those  objects  as 
real  external  and  internal  objects  to  God  as  their  creator? 
Suppose,  further,  that  we  have  precisely  similar  visions,  and  do 
not  and  cannot  know  whether  they  are,  in  fact,  mere  dream- 
visions  or  valid  perceptions  of  real  objects.  Should  we  not  still 
be  guilty  as  before  of  logically  dreaming,  if,  in  a  state  of  ac- 
knowledged ignorance  of  the  fact  whether  what  appears  as  ob- 
jects external  to  the  ego  are  real  external  objects  or  mere  crea- 
tions of  the  ego  itself,  we  reason  from  said  visions  as  valid  for 
the  reality  and  character  of  their  objects — as  objects  external 
to  the  mind — to  the  being  and  character  of  God  as  the  creator 
of  such  objects?  and  all  this  under  the  principle,  "Design  sup- 
poses a  designer  ?"  Whenever  we  reason  from  facts  of  the  ex- 
ternal universe  to  God,  as  the  author  and  arranger  of  said  uni- 
verse— and  that  under  the  principle,  "Design  supposes  a  de- 
signer,"— We  assume,  as  the  exclusive  basis  of  our  deductions, 
the  reality  of  said  universe,  and  the  objective  validity  of  our 
knowledge  of  the  same.  Take  away  this  one  assumption,  and 
nothing  is  left  for  us  to  reason  about;  nothing  whatever  is 
given  as  actually  created,  and  then  arranged  according  to  the 
principle  under  consideration.  If,  in  this  state  of  ignorance,  we 
proceed  to  reason  from  nature  to  nature's  God,  we  employ  a 


APPLIED     LOGIC.  367 

syllogism  not  merely  having  a  disputed  major,  but  no  valid  mi- 
nor at  all.  To  admit  and  affirm,  then,  that  such  is  the  exclusive 
character  of  our  knowledge  of  nature,  is  to  invalidate  utterly 
the  theistic  syllogism  as  employed  in  the  design  argument. 

What  has  our  author  done  in  respect  to  this  subject  ?  On 
this  subject  we  will  permit  him  to  speak  for  himself.  After  af- 
firming that  many,  to  say  the  least,  of  the  elements  of  our  im- 
pressions in  regard  to  external  nature  have  exclusively  a  sub- 
jective or  mental,  and  no  external  origin,  he  presents  the  fol- 
lowing questions  with  his  own  answers  to  them  annexed  : 

"  But  may  not  the  perceiving  mind  be  the  creator  of  its 
whole  world  of  perception  ?  It  gives  light  and  coloring  to  na- 
ture's picture,  may  it  not  be  the  author  also  of  the  outline  or 
shape,  and  of  the  invisible  network  which  receives  the  color- 
ing ?  Mind,  it  is  true,  is  distinguished  from  matter,  so  far  as 
we  can  see,  by  the  facts  of  the  will.  Yet  of  that  which  is 
known  as  matter,  something,  we  see,  comes  of  the  mind's  sensi- 
bility. May  not  this  faculty  be  the  origin  of  the  whole  ?  May 
not  all  the  laws  and  appearances  of  nature  be  evolved  from  a 
spontaneous  action  of  the  soul  according  to  the  laws  of  its  be- 
ing ?  May  not  life  be  a  self-consistent  dream  ?  It  is  a  suppos- 
able  theory  of  existence,  and  one  not  to  be  refuted  by  argu- 
ments, nor  quite  evaded  on  any  theory  of  perception.  We 
have  an  immediate  knowledge  of  the  self  and  the  world  ;  but 
so  long  as  it  is  only  relative — till  we  can  descend  beneath  phe- 
nomena to  realities — we  are  open  to  the  question,  May  not  the 
non-ego  be  presented  by  the  mind  to  its  self,  and  the  act  of  per- 
ception a  relation  between  one  faculty  and  another  ?" 

In  another  place,  when  speaking  of  the  theory  of  Berkley — 
which  denies  absolutely  the  existence  of  an  external  world,  of 
all  existences  external  to  finite  mind  but  God  himself— our  au- 
thor says,  "No  reasoning  can  refute  it,  nor  prove  it  to  be  im- 
possible in  the  nature  of  things.  It  is  quite  conceivable  that 
our  life  may  be  not  a  reality  but  a  dream,  of  which  the  figures 
and  visions  are  represented  according  to  certain  rules  and  un- 
changing laws  by  the  agency  of  a  superior  being."  Again : 
"  No  appeal  to  the  truth  of  God  or  the  common  sense  of  man- 


368  LOGIC. 

kind  can  wholly  set  aside  the  pretensions  of  the  idealist,"  &c. 
It  is  also  a  fundamental  doctrine  of  this  author,  that  we  have 
no  valid  knowledge  of  matter  or  spirit  either ;  that  we  do  not 
and  cannot  know  but  that  in  their  ultimate  essence  they  may 
he  one  and  the  same  substances.  "  All  our  immediate  know- 
ledge, it  will  be  seen,"  he  says,  "  is  relative  and  of  phenomena, 
not  of  real  being."  Again  :  "  We  cannot  know  that  any  di- 
vision of  conceptions  will  correspond  to  the  reality  of  things." 
Of  matter  and  spirit,  he  says,  that  they  are  "  two  things  which 
are  wholly  unknown  in  themselves."  "It  is  only  to  ws-that 
matter  is  massive,  heavy,  and  inert.  In  itself,  and  without  ref- 
erence to  the  senses,  it  may  be  conceived  to  be  as  spiritual  as 
even  spirit."  These  are  the  principles  and  dogmas  which  per- 
meate and  characterize  this  whole  production — principles  and 
dogmas  which  affirm  the  following  propositions  as  true : 

1.  We  have  and  can  have  no  valid  evidence  even  of  the  ex- 
istence of  any  finite  realities  external  to  the  mind  itself,  it  being 
absolutely  impossible  to  disprove  the  theory  of  idealism.  2.  Of 
such  realities,  if  they  do  exist,  we  have  and  can  have  no  form  of 
valid  knowledge — any  knowledge  by  which  we  can  even  deter- 
mine whether  such  objects  are  material  or  spiritual  in  their  na- 
ture. 3.  The  mind  itself  is  and  must  be  equally  unknown  to 
itself.  What  are  the  necessary  logical  consequences  of  such 
principles  ?  They  are  the  following,  among  others :  (l.)  We 
are  undeniably  doing  nothing  else  than  logically  dreaming — 
and  that  with  our  own  eyes  wide  open,  and  the  absurdity  of 
the  whole  procedure  visible  to  all  the  world — when  we  reason 
from  a  imiverse  that  we  admit  we  do  not  and  cannot  know  to 
exist  at  all,  to  a  really  existing  creator  and  governor  of  said 
universe.  If  we  cannot  prove  idealism  false,  we  cannot  prove 
theism  true.  Without  logical  inconsistency  we  cannot  assume 
any  other  ground  than  that  of  skepticism,  and  moral  integrity 
requires  us  to  admit  the  fact.  (2.)  Equally  absurd  is  it  to 
present  cognitions  which  we  "  cannot  know  to  correspond  with 
the  reality  of  things" — and  whose  utter  want  of  objective  va- 
lidity Ave  admit — as  the  basis  of  deductions  in  regard  to  the  re- 
lations of  such  things  to  any  other  reality  or  realities  whatever, 


APPLIED     LOGIC.  369 

and  above  all  as  the  only  basis  of  a  proof  of  the  being  and  per- 
fections of  God.  A  court  of  justice  would  cover  itself  with  uni- 
versal reprobation,  which  should  upon  such  evidence  impose 
upon  any  man  a  fine  of  six  cents.  Yet  such  cognitions,  our  au- 
thor affirms,  present  all  the  evidence  we  have  of  the  validity  of 
the  fundamental  doctrine  of  all  religion.  (3.)  All  the  deity 
such  cognitions  can  in  any  case  give  us,  is  an  unknown  and 
unknowable  something — sustaining  unknown  and  unknowable 
relations  to  unknown  and  unknowable  somethings,  called,  for 
convenience,  matter  and  spirit.  Any  skeptic  whatever  may 
readily  admit  all  the  valid  logical  deductions  of  our  author's 
system  as  expounded  by  himself,  and  not  abandon  any  one  arti- 
cle of  his  faith.  (4.)  In  using  the  design  argument  in  proof  of 
the  being  and  perfections  of  God,  our  author,  we  remark  in  the 
next  place,  einploys  a  syllogism  with  a  disputed  major,  and  a 
minor  which  he  himself  has'  proven — if  we  admit  the  truth  of 
his  previous  deductions — to  be  utterly  void  of  validity.  In 
other  words,  he  has  first  laid  down  a  principle — "  Design  sup- 
poses a  designer" — which  every  skeptic  disputes,  and  then 
ranged  under  that  principle  cognitions  which  he  himself  affirms 
to  be  utterly  void  of  objective  validity,  and  all  this  as  the  basis 
of  the  proof  of  being  of  God.  (5.)  In  the  conduct  of  his  argu- 
ment under  this  syllogism,  our  author  assumes  that  these  cogni- 
tions— previously  affirmed  to  be  invalid  objectively — have  ob- 
jective as  well  as  subjective  validity,  and  the  whole  procedure 
presents  naught  but  the  aspect  of  absurdity  when  we  drop  that 
assumption.  What  conceivable  bearing  have  the  extent  of 
creation,  the  asteroids,  and  other  heavenly  bodies ;  what  have 
the  harmony,  diversity,  and  beauty  of  nature  to  do  in  regard 
to  this  subject,  but  upon  the  assumption  that  these  are  known 
realities  ?  Admit  that  this  vast  universe,  for  aught  that  we  do 
or  can  know,  is  naught  but  "  the  baseless  fabric  of  a  vision," 
— and  this  is  precisely  what  our  author  would  have  us  affirm  of 
it — and  what  valid  evidence  does  it  then  afford  of  the  existence 
of  any  power  out  of  and  above  the  unknown  and  unknowable 
something  called  mind,  which,  for  aught  that  we  do  or  can 
know,  is  the  exclusive  creator  of  the  whole  fabric  before  us  ? 
16* 


370  LOGIC. 

(6.)  Our  author,  we  remark  finally  in  this  connection,  was  logi- 
cally bound  by  his  own  fundamental  principles  and  assumptions 
to  deny  absolutely  the  possibility  of  valid  knowledge  on  any 
subject  whatever,  and  thus  to  ignore  the  whole  subject  of  his 
treatise  as  far  as  the  use  of  the  logical  faculty  is  concerned. 
When  we  make  use  of  cognitions  as  the  basis  of  deductions,  the 
former  become  themselves  the  objects  of  cognition.  Our  cog- 
nitive faculty,  our  author  affirms,  does  not,  as  far  as  we  do  or 
can  know,  cognize  any  reality  as  it  is.  What  validity,  then, 
has  its  procedures  when  its  own  operations  are  made  the  ob- 
jects of  cognition,  and  the  cognitions  thus  obtained  are  made 
the  basis  of  scientific  deductions?  In  all  such  cases,  all  our 
procedures  have,  and  must  have,  more  and  more  palpable  char- 
acteristics of  absolute  invalidity.  We  begin  with  that  which 
has  mere  subjective  validity,  and  end  with  what  is  not  likely  to 
have  any  form  of  validity,  objective  or  subjective. 

All  the  above  conclusions  are  further  confirmed  by  Mr.  Thom- 
son's own  statements  of  the  consequences  of  his  own  principles, 
and  of  the  nature  of  the  theistic  problem  as  understood  by  him- 
self. "  Let  it  be  granted,"  he  says,  "  that  nature,  as  manifested 
in  .the  soul  and  in  the  world,  is  the  province  of  reason.  Yet  in 
itself  it  is  unknown.  Reason  is  obliged  to  regard  it  •  as  the 
manifestation  of  occult  causes,  and  is  compelled,  as  we  have 
seen,  to  make  its  choice  between  one  and  many  incomprehensi- 
bles.  It  demands  an  unknown  substratum  of  the  visible,  and 
an  unknown  essence  of  the  intelligent ;  and  may  thus  be  led 
to  an  unknown  cause  of  both,  wherein  to  find  the  cause  and  ex- 
planation of  their  marvellous  relationship." 

We  venture  the  affirmation,  that  no  skeptic  can  make,  or 
would  desire  to  make,  a  more  distinct  and  explicit  statement  ot 
his  own  principles  and  deductions,  than  Mr.  Thomson  has  here 
made  for  him.  When,  from  the  sphere  of  our  own  conscious 
mental  operations,  we  advance  into  that  of  realities  subjective 
or  objective,  we  are  exclusively,  says  the  skeptic,  in  the  regions 
of  the  wholly  unknown.  So  says  Mr.  Thomson.  As  many 
hypotheses  of  immediate  and  ultimate  causation  here  present 
themselves,  each  and  all  equally  consistent  with  all. the  facts, 


APPLIED     LOGIC.  371 

each  alike  must  be  held  as  only  possibly  true ;  and  if  we  would 
assume  either  as  true,  we  must,  says  the  skeptic,  act  without 
valid  reason — "  choosing  one  among  many  incomprehensible^." 
So  says  Mr.  Thomson.  The  real  cause  of  the  ego  and  of  the 
non-ego,  says  the  skeptic,  is  and  must  be  unknown.  So  says 
Mr.  Thomson.  As  this  cause  is  and  must  be  wholly  unknown, 
no  one  hypothesis  relative  to  its  character  can  have  any  logical 
preference  over  any  of  the  others  referred  to.  So  says  Mr. 
Thomson.  "  We  are  compelled  to  make  choice  between  one 
and  many  incomprehensibles." 

The  nature  of  the  deductions  which  Mr.  Thomson  professed- 
ly reaches  in  respect  to  the  being  and  character  of  God,  are  in 
full  accordance  wTith  his  principles.  As  the  cognitions  from 
which  he  reasons  have,  as  he  professes,  only  subjective  validity, 
the  same  must  be  equally  true  of  their  consequences.  Such  ex- 
clusively is  the  character  of  his  theistic  deductions  as  given  by 
himself.  "  We  speak,"  he  says,  "  of  a  certain  relation  to  our- 
selves when  we  say  of  matter  that  it  is  hard.  We  do  the  same 
thing  when  we  say  of  God  that  he  is  good.  When  he  is  said 
to  be  powerful,  it  is  meant  that  he  reveals  himself  to  us  in 
works,  which,  in  human  thought,  are  works  of  power,"  &c. 
Mr.  Thomson,  we  should  remember,  does  not  profess — and  his 
principles  do  not  allow  him  to  profess — to  find  a  real  God  of 
ascertained  attributes  of  any  kind.  The  skeptic  may  accept  of 
every  one  of  his  deductions,  as  explained  by  Mr.  Thomson  him- 
self, and  not  change,  in  the  least,  one  of  his  own  principles  and 
deductions ;  and  the  true  believer  can  say  to  Mr.  Thomson  in 
truth,  You  have  taken  from  my  heart  and  my  intelligence  both 
my  God,  and  placed  him  where  he  can  never  be  found,  or 
known  if  he  was  found. 

Mr.  Thomson  has  also  himself  shown  the  skeptic  how  he  may, 
upon  purely  scientific  grounds — grounds  which  Mr.  Thomson 
admits  to  be  valid  from  his  own  principles — escape  all  theistic 
deductions  of  every  kind  : 

"  From  a  theology  founded  on  the  foregoing  principles,  the 
atheist,"  he  says,  "  may  find  an  outlet  in  total  skepticism.  If 
it  be  demonstrated  that  our  knowledge  of  the  Supreme  Being 


372  LOGIC. 

is  as  valid,  and  not  less  inadequate  than  that  of  an  external 
"world,  he  may  then  have  the  hardihood  to  affirm  that  both 
knowledges  are  illusive,  and  all  philosophy  impossible.  He 
may  deny  that  we  have  as  yet  attained  any  strict  cognition 
either  of  the  soul  or  of  the  world,  as  dependent  or  inde- 
pendent in  existence.  "We  see,  indeed — this  is  indisputable — 
that  the  world  is  not  dependent  in  existence  upon  that  con- 
scious energy  of  the  soul  which  we  call  will.  But  may  it  not 
be  evolved  by  a  spontaneous  energy  of  our  nature,  lying  be- 
yond the  reach  of  consciousness  and  independent  of  the  will  ? 
The  s]3ringing  up  of  our  own  existence,  it  may  be  alleged,  is 
beyond  the  consciousness  and  out  of  the  sphere  of  the  volition. 
Or  again,  the  materialist  may  assign  real  existence  to  matter, 
and  make  mind  to  be  but  a  certain  evolution  from  it,  or  a  hap- 
py result  of  organization.  Or,  he  may  affirm  that  many  con- 
ceivable theories  have  not  been  confuted. 

"  Granted.  We  profess  to  find  in  the  foregoing  observations 
a  basis  for  the  demonstration  that  our  knowledge  of  the  Infinite 
Being  is  as  valid  as  that  of  the  finite.  If  the  question  is  to  be 
pressed  further,  it  must  be  admitted  assuredly  that  the  depths 
of  being  are  unfathomable.  Whether,  in  the  absolute  nature 
of  things,  the  mind  is  wholly  distinct  from  the  world  or  in  any 
way  related  to  it,  is  beyond  the  province  of  man's  intelligence. 
It  cannot  be  seen  how  things  which  do  appear,  flow  forth  from 
the  fountain  of  existence." 

The  skeptic  can  ask  no  more,  and  does  ask  no  more,  than  is 
here  granted  him,  and  that  upon  professedly  scientific  grounds. 
ISTow,  if  the  skeptic  may  upon  scientific  grounds  affirm  all  this, 
then  theism  undeniably  can  be  held  as  true  upon  no  scientific 
grounds. 

Mr.  Thomson,  we  remark  again,  refutes  the  claims  of  mate- 
rialism upon  the  exclusive  assumption  of  the  validity  of  the 
skeptical  hypothesis,  and  upon  grounds,  too,  utterly  subversive 
of  the  claims  of  theism.  As  matter  and  spirit  are  wholly  un- 
known to  us  as  substances,  we  cannot-  affirm — such  is  his  ar- 
gument— as  materialism  does,  that  one  is  the  other.  "  Two 
things,"  he  says,  "which  are  wholly  unknown  in  themselves 


APPLIED     LOGIC.  373 

cannot  be  known  to  exist  in  the  same  way,  or  with  any  com- 
munity of  properties  or  attributes."  Very  true,  replies  the 
skeptic,  and  for  the  reason  here  stated — materialism  may  be 
true.  Of  two  things  wholly  unknown,  you  cannot  say  that 
they  do  not  exist  in  the  same  way,  and  with  an  absolute  com- 
munity of  properties  and  attributes.  Further,  of  two  such 
things,  you  caimot  know  that  they  sustain  any  relations  to  any 
third  reality  whose  existence  even  can  be  revealed  only  through 
these.  Of  such  things,  you  cannot  know  that  they  are  or  are 
not  created  and  controlled  substances  at  all,  and,  consequently, 
that  any  such  creator  or  governor  exists.  Mr.  Thomson  must 
renounce  his  first-  principles — the  validity  of  the  sensational 
theory  of  external  perception — or  accept  of  these  deductions  in 
their  fullest  extent. 

The  nature  and  kind  of  validity  which — in  his  own  estima- 
tion— does  attach  to  Mr.  Thomson's  demonstration  of  the  exist- 
ence and  character  of  God,  should  not  be  overlooked  in  tins 
connection.  Our  knowledge  of  God,  he  teaches,  has  the- same 
and  no  other  validity  than  that  winch  attaches  to  our  know- 
ledge of  nature.  This  is  directly  expressed  in  the  extracts 
above  given,  and  often  affirmed  and  reiterated  in  the  treatise 
before  us.  What  then  is  the  theistic,  and  what  is  the  skeptical 
syllogism  on  this  subject  ?  and  in  which  do  we  find  our  author  ? 
The  theistic  syllogism  is  this  : 

If  we  have  valid  knowledge  of  the  existence  and  character  of  the  finite,  we 

have  a  similar  knowledge  of  the  Infinite  : 
"We  have  such  knowledge  of  the  finite  ; 
We  have,  therefore,  a  similar  knowledge  of  the  Infinite. 

The  skeptical  syllogism  is  this : 

If  we  have  no  valid  knowledge  of  the  existence  and  character  of  the  finite, 

we  have  and  can  have  no  such  knowledge  of  the  Infinite  ; 
We  have  no  such  knowledge  of  the  finite  ; 
We  have  and  can  have,  therefore,  no  such  knowledge  of  the  Infinite. 

Mr.  Thomson's  principles  and  deductions  in  respect  to  the 
finite,  place  him  undeniably  within  the  exclusive  sphere  of  the 
latter  syllogism,  and  it  is  only  by  a  renunciation  of  the  funda- 


374  LOGIC. 

mental  principle  of  his  philosophy  of  nature,  that  he  can  possi- 
bly get  into  the  former. 

Let  us  now  contemplate  Mr.  Thomson's  own  estimate  of  the 
real  character  of  the  evidence  which  exists,  and  which  he  has 
to  offer,  in  proof  of  this  great  fundamental  truth  of  all  religion. 
After  professedly  showing  us  that  we  have  no  valid  evidence 
that  there  is  any  created  universe — matter  and  spirit  as  they 
are,  being  both  alike  absolutely  unknown  to  us — after  saying 
that  "  to  a  mind  which  has  not  been  initiated  in  the  difficulties 
of  skepticism,  all  nature  declares  with  the  unanimous  voice  of 
ten  thousand  tongues,  There  is  one  God,  the  Father  of  all ;" 
after  saying  that  "  in  examining  the  evidences  of  this  truth,  and 
inquiring  whether  this  voice  be  credible,  we  become  aware  of 
the  wide  difference  which  exists  between  truth  as  it  is  in  itself, 
and  truth  as  it  becomes  known  to  the  mind  of  man,"  he  says, 
"  The  method  of  theism  is  therefore  humble,  and  such  as  be- 
comes man  on  such  a  subject."  The  real  meaning  of  the  term 
"humble"  can,  in  the  present  connection,  hardly  be  deemed 
doubtful.  It  can  mean  nothing  else,  as  it  appears  to  us,  than 
this — inconclusive  on  scientific  grounds.  Religion  or  theism 
addresses  us  in  tones  of  authority  the  most  absolute  conceiva- 
ble, "  Thou  shalt  have  no  other  gods  before  me," — "  Thou  shalt 
worship  the  Lord  thy  God,  and  him  only  shalt  thou  serve," — 
You  know  God,  and  shall  worship  him  as  God,  &c.  When 
humbly  asked  for  the  evidence  of  the  validity  of  these  high 
claims,  her  tone,  as  interpreted  by  Mr.  Thomson,  is  suddenly 
changed.  Her  voice  is  now  very  humble.  Theism  appears 
now  only  as  "  one  •  among  many  incomprehensibles,"  each  of 
which  has  upon  scientific  grounds  equal  claims,  and  each  in  dis- 
tinction from  the  other  having  no  claims  at  all.  Now  we  en- 
ter our  solemn  protest  against  such  a  presentation  of  the  claims 
of  our  holy  religion.  We  boldly  affirm  that  religion  is  as  able 
to  meet  fully  the  logical  demands  of  our  nature  as  any  other, 
and  is  able  to  meet  them  all  perfectly.  On  account  of  such 
presentations  as  the  above,  we  are  free  to  say,  that  we  regard 
the  production  before  us  as  one  of  the  most  dangerous  books  of 
modern  times,  especially  when  we  consider  the  circumstances 


APPLIED     LOGIC.  375 

in  which  it  comes  before  the  world.  We  solemnly  believe, 
that  no  anti-theist  has  produced  a  work  so  adapted  to  confirm 
immovably  the  doubts  of  the  skeptic,  and  to  unsettle  the  faith 
of  the  believer,  as  this. 

The  character  of  Mr.  Thomson's  treatise,  we  remark  in  the 
last  place,  is  the  necessary  logical  consequence  of  the  theory  of 
external  perception  which  he  has  laid  at  the  foundation  of  all 
his  deductions — the  sensational  theory.  If  all  our  knowledge 
of  external  nature  is  indirect  and  mediate,  and  exclusively  de- 
rived through  one  medium — sensation ;  if  we  have  and  can 
have  no  real  or  presentative  knowledge  of  the  self  or  of  the 
not-self,  then,  indeed,  as  we  have  before  shown,  mind,  matter, 
and  God  must  be  alike  unknown  and  unknowable  realities  to 
us,  and  skepticism  is  the  only  true  philosophy  of  the  finite  and 
of  the  Infinite.  If  we  attempt  to  reason  about  either,  we  shall 
find  ourselves  eternally  tempest-tossed  upon  a  boundless  chaos 
of  conflicting  hypotheses,  each  pressing  questions  upon  us  which 
neither  it,  nor  either  of  the  others,  can  ever  resolve ;  every  de- 
duction apparently  reached  will  be  found  at  last  to  have  been 
settled  upon  grounds  more  debatable  than  the  original  issues, 
and  we  shall  retire  from  the  conflict  with  but  one  impression 
resting  upon  our  minds,  to  wit,  that  nature  itself  is  a  lie,  and 
that  he  that  thinks  the  least  is,  of  all  men,  the  wisest,  and  at 
the  furtherest  remove  from  error. 

Of  the  two  treatises  which,  for  the  sake  of  science  and  reli- 
gion, we  have  thus  freely  criticised,  we  should  say  that  the 
former,  in  its  relation  to  the  doctrine  of  method,  in  the  articles 
of  definition,  logical  division  and  arrangement  of  topics,  and 
distinctness  and  force  in  the  statement  of  thought,  as  nearly 
realizes  the  idea  of  science  as  almost  any  treatise  that  we  have 
met  with  on  any  subject;  while  the  latter  is  one  of  the  most 
fragmentary  productions,  and  the  least  systematic  even  in  the 
arrangement  of  the  fragments,  that  we  ever  read.  Both  au- 
thors have,  in  the  development  of  the  theistic  argument,  erred 
fundamentally  in  basing  said  argument  upon  the  deductions 
of  certain  disputed  theories  in  respect  to  the  origin  of  know- 
ledge. 


THE   DOGMA   THAT   OUR   IDEA    OF    GOD   IS   PURELY   NEGATIVE. 

Among  a  large  class  of  thinkers,  it  has  now  come  to  be  re- 
garded as  a  first  truth  in  science,  that  our  idea  of  God  is  purely 
negative,  the  elements  constituting  it  being  mere  negations  of 
the  finite.  In  regard  to  this  dogma  we  would  simply  drop  the 
following  suggestions,  and  leave  them  for  the  reflection  of  the 
reader : 

1.  This  dogma  is  based  upon  an  undeniable  psychological 
error,  a  false  analysis  of  the  idea  itself  as  given  in  consciousness. 
No  individual,  from  a  careful  analysis  of  the  idea  as  thus  given, 
would  ever  come  to  any  such  conclusion  in  respect  to  it.  What 
are  the  elements  which  do,  as  a  matter  of  fact,  enter  into  it  ? 
In  the  first  place,  we  conceive  of  God  as  a  being  actually  exist- 
ing. So  far  our  conception  of  him  is,  undeniably,  as  positive 
as  any  other  which  we  can  have  of  any  object  whatever.  In 
the  next  place,  we  conceive  of  him  as  a  real  cause — the  actual 
ultimate  cause  of  all  that  exists  conditionally.  Now  no  ideas 
are  more  positive  than  those  of  causation,  and  our  ideas  of  ulti- 
mate are  just  as  positive  as  are  our  ideas  of  proximate  causa- 
tion. Again,  we  conceive  of  God  as  a  self-conscious  personali- 
ty, having  an  absolute  knowledge  of  himself  and  all  other  reali- 
ties. No  element  more  positive  does  or  can  enter  into  any  con- 
ception whatever.  Now  when  we  attach  the  idea  of  infinity 
and  perfection  to  each  of  the  divine  attributes,  we  do  not  there- 
by annihilate  the  positive  elements  in  the  general  idea  itself, 
and  change  the  character  of  the  whole  from  the  positive  to  the 
negative  form.  The  positive  does  not,  by  mere  enlargement, 
like,  circles  in  the  water,  "  vanish  into  naught." 

2.  This  dogma  is  based  upon  a  total  misconception  of  the  na- 
ture and  sphere  of  negation.  Negation  is  always,  and  from  the 
nature  of  the  case  must  be,  subsequent  to  affirmation.  The 
former  has  its  exclusive  basis  in  the  latter.  To  deny  a  given 
attribute  of  any  object — as  A  of  B,  for  example — implies  that 
the  two  are  known  to  the  mind,  and  that  the  known  attributes 
of  A  are  perceived  to  be  incompatible  with  the  existence  of 
B  in  the  same  subject.     To  deny  limitation  of  God  implies 


APPLIED     LOGIC.  377 

(1.)  that  we  know  him  as  existing;  and  (2.)  as  possessed  of 
attributes  incompatible  with  the  idea  of  limitation.  The  dog- 
ma of  a  negative  concept  of  any  reality  whatever  is  a  pure 
absurdity. 

3.  This  dogma,  we  remark  once  more,  is  utterly  subversive 
of  all  religion.  "  Ex,  nihil,  nihil  Jit."  The  commands,  prohi- 
bitions, and  teachings  of  religion  are  all  positive,  absolute,  and 
the  idea  of  God  lies  at  the  basis  of  them  all.  From  mere  ne- 
gation— if  it  could  exist  as  a  concept — nothing  positive  can  pro- 
ceed. A  god  represented  by  "  a  bundle  of  negations," — the 
expression  used  by  a  distinguished  author  to  express  our  idea 
of  God — can  no  more,  nor  so  much,  be  an  object  of  fear,  love, 
reverence,  &c,  than  infinite  space.  With  a  mere  negative  idea 
of  God,  if  we  could  have  such  a  concept  of  him,  religion  with 
its  absolute  teachings  would  be  an  absurdity,  and  nothing  else. 

THE   REAL   BASIS    OF   ALL   VALID    SCIENTIFIC   PROCEDURES. 

With  certain  individuals  who  assume  to  themselves  the  pos- 
session of  the  highest  forms  of  wisdom,  it  is  not  uncommon  to 
decry  science  and  to  deny  the  possibility  of  philosopliy. 

"  Science,"  says  Professor  Lewis,  "  has  indeed  enlarged  our 
field  of  thought,  and  for  this  we  will  be  thankful  to  God  and  to 
scientific  men.  But  what  is  it  after  all  that  she  has  given  us,  or 
can  give  us,  but  a  knowledge  of  phenomena — appearances  ? 
What  are  her  boasted  laws,  but  generalizations  of  such  phe- 
nomena ever  resolving  themselves  into  some  one  great  fact 
that  seems  to  be  an  original  energy,  whilst  evermore  the  appli- 
cation of  a  stronger  lens  to  our  analytical  telescope  revolves 
such  seeming  primal  force  into  an  appearance  or  manifestation 
of  something  still  more  remote,  which  in  this  way,  and  in  this 
way  alone,  reveals  its  presence  to  our  senses.  Thus  the  course 
of  human  science  has  ever  been  the  substitution  of  one  set  of 
conceptions  for  another.  Firmaments  have  given  place  to  con- 
centric spheres,  spheres  to  empyreans,  empyreans  to  cycles  and 
epicycles,  epicycles  to  vortices,  vortices  to  gravities  and  fluids, 
ever  demanding  for  the  theoretic  imagination  other  fluids  as 


378  LOGIC. 

the  only  conditions  on  which  their  action  could  be  made  con- 
ceivable." 

Why  does  this  author  give  us  such  a  view  of  the  scientifip 
procedure  ?  Simply  on  account  of  his  theory  of  external  per- 
ception— the  sensational  theory — which  gives  us  nothing  but 
shadows  of  we  know  and.  can  know  not  what.  When  we 
attempt  to  cognize  scientifically  these  shadows,  new  shadows 
present  themselves  which  convert  original  cognitions  into  mere 
appearances ;  and  so  on  forever  without  any  nearer  approach 
to  truth  being  made.  Science  may  change  our  modes  of  think- 
ing, but  can  never  add  to  our  stock  of  real  knowledge.  This 
is  science  according  to  the  sensational  theory. 

Let  us  now  suppose  that  we  originally  obtain,  not  shadows  of 
things  unknown,  but  real  valid  presentative  and  representative 
intuitions,  together  with  the  logical  antecedents  of  the  same — 
of  internal  and  external  realities  themselves.  What  we  have 
gained  is  then  an  eternally  enduring  acquisition.  Subsequent 
investigations  may  add  new  elements  to  these  cognitions ;  sepa- 
rate erroneous  ones,  which,  by  assumption,  may  be  introduced 
into  them,  may  abstract  the  elements  which  constitute  said  cog- 
nitions, and  classify  and  arrange  them  accordingly,  &c.  The 
progress  of  science  is  not  the  substitution  of  one  shadow  for 
another,  but  a  perpetual  accumulation  of  imperishable  treasures. 
The  thinker  who  sneers  at  science  and  denies  the  possibility  of 
philosophy,  has  himself  been  deluded  by  a  false  philosophy  into 
the  belief  that  he  is  looking  only  at  shadows,  when,  in  fact,  he 
is  beholding  with  open  face  realities  as  they  are.  The  sciences 
have  not  a  phenomenal,  but  a  real  basis,  and  are,  when  rightly 
conducted,  the  valid  interpreters,  not  of  appearances,  in  which 
nothing  appears,  but  of  truth  itself. 


THE  DOGMA  THAT  OUR  KNOWLEDGE  OF  NATURE  IS  CONFINED 
TO  PHENOMENA,  AND  DOES  NOT  PERTAIN  TO  SUBSTANCES 
THEMSELVES. 

Ages  commonly  intervene  before  the  mind  fully  emancipates 
itself  from  the  influence  of  false  assumptions,  which  it  has  for- a 


APPLIED     LOGIC.  379 

time  employed  as  first  truths.  This  is  emphatically  true  of  the 
dogma  above  stated.  According  to  its  real  import  there  are, 
in  respect  to  mind  and  external  nature,  three  classes  of  reali- 
ties— the  mind  which  perceives  ;  external  substances  never  per? 
ceived  or  known  at  all ;  and  a  tertium  quid,  phenomena,  exist- 
ing between  the  two  realities  named  and  themselves,  the  exclu- 
sive objects  of  perception  and  knowledge.  Now  it  should  be 
borne  in  mind  that  there  are  but  two  classes  of  perceptions,  the 
presentative  and  the  representative.  In  the  latter,  nothing 
whatever  external  to  the  mind  is  perceived,  but  simply  and  ex- 
clusively a  mental  state,  a  sensation,  or  the  mind  itself  in  thai 
state.  The  external  object  is  the  unperceived  cause  of  the  sen- 
sation, and  the  latter  the  perceived  effect  of  said  cause.  In  this 
case,  there  is  no  third  thing  between  the  percipient  and  the 
thing  perceived.  In  presentative  perception  of  an  external  ob- 
ject, the  thing  perceived  is  the  object  itself,  so  far  forth  as  it  or 
any  thing  relating  to  it  is  perceived  at  all.  We  never  perceive 
the  whole  object,  but  so  far  as  it  is  presentatively  perceived  at 
all,  the  phenomenon  and  object,  or  substance,  are  one  and  iden- 
tical. In  reference  to  presentative  perception,  therefore,  the 
principle  holds  universally,  that  substances  are  as  their  phe- 
nomena. In  representative  knowledge,  external  substances  are 
the  unknown  causes  of  known  sensitive  states — sensations.  In 
presentative  knowledge  of  such  objects,  substances — substances 
themaelves — are  the  known  objects  of  known  intellectual  states, 
to  wit,  perceptions.  The  doctrine  of  appearances  in  which 
realities  themselves  do  not  appear,  should,  by  this  time,  be  ex-, 
eluded  from  the  domain  of  science. 


THE  DOGMA  THAT  INDIVIDUAL  CONCEPTIONS  PERTAIN  TO  OB- 
JECTS, AND  GENERAL  ONES  ONLY  TO  THE  MIND  WHICH 
FORMS    THEM. 

It  is  now  commonly  assumed  as  a  principle  in  science,  that 
while  individual  conceptions  pertain  to  objects,  general  ones — 
the  specifical  and  generical — pertain  exclusively  to  the  mind 
which  forms  them  for  its  own  convenience.     It  is  deemed  im 


portant  that  we  should  understand  distinctly  hi  what  sense  this 
maxim  is  and  is  not  true.  In  illustration,  let  A  represent  the 
individual  conception  of  some  object,  John,  B  a  specifical,  C  a 
generical,  conception,  of  the  same  person.  .  Whatever  is  im- 
plied in  A,  or  in  any  element  of  the  same,  is' true  of  John.  The 
same  holds  equally  of  B  and  C.  The  only  difference  is  this  :  A 
represents  in  the  concrete  what  is  true  of  him  only ;  B  repre- 
sents what  is  equally  true  of  him,  but  what  is  also  true  of  a 
large  number  of  other  individuals ;  and  C  what  is  true  of  him  in 
common  with  a  still  wider  circle.  B  and  C,  then,  pertain  to 
the  individual  as  really  and  truly  as  A  does,  only  in  different 
relations — A  on  the  principle  of  exclusion,  and  B  and  C  on  that 
of  inclusion.  Without  explanation,  therefore, — an  explanation 
which  renders  the  thing  explained  almost,  if  not  quite  meaning- 
less— the  maxim  before  us  tends  only  to  "  darken  counsel  by 
words  without  knowledge." 

THE   IDEA    OF   A    "  POSITIVE   PHILOSOPHY." 

Some  of  the  greatest  ideas  that  ever  enter  the  human  mind 
are  not  unfrequently  first  presented  to  the  world  in  connection 
with  systems  of  error,  and  are,  for  that  reason,  for  a  time  at 
least,  regarded  by  the  friends  of  truth  as  meteors  of  darkness, 
and  not  as  being  what  in  reality  they  are,  great  central  suns  in 
the  firmament  of  science  and  of  truth.  Such  an  idea  has  been 
announced  to  the  world  in  the  title  of  a  work  embodying 
naught  almost  but  fundamental  error.  We  refer  to  the  phrase, 
"  The  Positive  Philosophy."  All  thinking  of  every  kind  is  pos- 
itive. To  think  is  to  affirm — to  affirm  the  presence  or  absence 
of  some  positive  attribute  in  some  positive  subject.  All  denial 
is  positive — to  affirm  incompatibility  of  two  positive  things,  or 
to  affirm  the  absence  in  a  known  object,  of  some  known  attri- 
bute. Till  an  object  is  known,  and  so  far  only  as  it  is  known, 
can  we  deny  any  thing  of  it,  thus  separating  the  known  from 
the  known.  The  dogma  of  a  purely  negative  conception  of 
any  object  is  one  of  the  absurdities  of  "  science  falsely  so  called." 
To  have  a  purely  negative  idea  we  must  cease  to  think  at  all, 


APPLIED     LOGIC.  381 

that  is,  have  no  thought  whatever.  The  "  positive  philosophy" 
assumes,  that  relatively  to  some  realities,  at  least,  mind  is  a 
faculty,  and  they  objects  of  real  valid  knowledge,  and  professes 
to  determine  the  extent,  limits,  objects,  laws,  and  tests  of  such 
knowledge.  It  may,  therefore,  be  defined  the  science  of  the 
thinkable,  its  object  being  to  give  upon  scientific  grounds  the 
answer  to  the  question,  "What  can  I  know  ?"  We  will  ven- 
ture the  expression  of  a  few  suggestions  in  regard  to  the  prin- 
ciples in  conformity  to  which  such  a  system  should  and  must 
be  developed.     On  this  subject  we  remark  : 

1.  In  developing  such  a  system  the  first  thing  to  be  done, 
as  we  suppose,  would  be  clearly  to  define  and  distinguish  two 
conceptions — a  mystery  and  absurdity.  The  former  would 
be  shown  to  imply  a  fact  known  to  exist,  while  the  cause, 
or  grounds,  or  both  together,  of  its  existence,  is  unknown  and 
unknowable  to  us.  The  latter  refers  to  statements  relatively 
to  matters  of  fact  coming  under  the  principle  of  contradiction 
— statements  in  which  the  same  things  are  aflirmed  and  denied 
of  the  same  object.  ISTo  facts  of  the  latter  class  can  occur. 
Any  facts  whatever  of  the  former  class,  for  aught  that  we  know 
or  can  know,  may  occur. 

2.  Existence  in  all  its  forms,  actual  and  conceivable,  would 
be  distinctly  recognized  as  a  mystery,  but  no  absurdity.  A 
priori  we  cannot  tell  what  does  exist,  nor  in  what  state  it 
exists.  Whatever  then  is  manifested  as  existing  must  be  rec- 
ognized as  a  reality.  The  question  of  its  existence  is  to  be  con- 
sidered as  forever  settled  by  the  fact  of  its  actual  manifestation. 
When  any  reality  is  manifested  as  existing,  its  existence  as  a 
fact  is  not  only  to  be  admitted,  but  also  that  of  all  realities 
necessarily  supposed  by  such  fact.  If,  for  example,  we  admit 
the  actual  existence  of  body,  we  must  admit  the  objective  reali- 
ty of  space ;  for  the  reason,  that  the  latter  not  being,  the  former 
could  not  be.     So  in  all  other  instances. 

3.  The  condition  of  the  possibility  of  knowledge  is  the 
actual  existence  of  a  subject  sustaining  to  actual  realities  the 
relation  of  a  power,  while  they  sustain  to  it  that  of  an  object 
of  real  knowledge,  and  these  two  in  such  relations  to  each 


382  logic. 

other  that  actual  knowledge  arises  in  consequence  of  this  cor- 
relation. 

4.  The  sphere  of  the  conceivably  knowable  is  all  realities  as 
they  are,  with  all  their  properties,  laws,  and  relations ;  that  of 
the  actually  knowable  in  any  given  case*,  depends  upon  the 
question  how  far  this  correlation  obtains,  in  fact,  in  said  case. 

5.  We  can  never  determine  d  priori  whether  such  power 
does  exist  in  any  given  case,  or  what  is  its  sphere,  any  more 
than  we  can  thus  determine  what  realities  do  and  do  not  exist. 
The  existence  of  a  power  of  knowledge  can  be  manifested  but 
by  its  actual  exercise,  and  the  question,  What  can  we  know  ? 
can  be  answered  but  through  these  two,  to  wit,  What  do  we 
know  ?  and,  What  is  implied  in  this  knowledge  ? 

6.  There  are  but  three  conceivable  forms  in  which  any  reali- 
ty can  be  known  to  us,  to  wit,  presentatively,  representatively, 
and  impliedly — that  is,  it  may  be  to  the  knowing  faculty  an  ob- 
ject of  direct  and  immediate  perception,  or  an  unknown  cause 
of  a  known  state  of  the  sensibility,  or  necessarily  presupposed 
as  the  condition  of  the  existence  of  that  which  is  known  to  be.  • 

7.  In  determining  our  theory  of  existence — that  is,  of  reali- 
ties as  actually  existing — we  are  to  hold  ourselves  as  bound  to 
admit  nothing  as  real,  which  is  not  manifested  in  one  or  the 
other  of  the  above-named  forms  as  actually  existing.  On  the 
other  hand,  we  are  bound  by  the  principles  of  intellectual  and 
moral  integrity,  to  admit  as  real  all  forms  of  existence  thus 
manifested,  and  as  manifested.  Nothing  is  to  be  admitted  as 
actual  which  is  not  thus  known,  and  all  that  is  thus  known 
must  be  admitted  as  actual.  The  objects  of  presentative  know- 
ledge with  their  logical  antecedents  are  to  be  held  as  really 
known,  that  is,  known  as  they  are,  and  those  of  representative 
knowledge  with  their  logical  antecedents  as  relatively  known. 

8.  In  determining  what  realities  do  exist  from  what  we  know 
to  exist,  the  following  systems  present  themselves.  We  may 
suppose  that  the  knowing  faculty  has  an  actual  presentative 
knowledge  of  mind — the  subject,  on  the  one  hand,  and  of  the 
external  universe  or  matter,  on  the  other.  This  gives  us  the 
system  of  realism.    We  may  suppose  again,  that  matter  is  the 


APPLIED     LOGIC.  383 

only  object  of  such  knowledge,  and  hence  resolve  all  realities 
into  it — the  system  of  materialism.  Or  we  may  suppose  that 
there  is  "  a  synthesis  of  being  and  knowing,"  that  presentative 
knowledge  pertains  exclusively  to  mental  states.  All  known 
realities  are  consequently  to  be  resolved  into  such  states,  and 
here  we  have  three  theories.  If  the  cause  of  the  mind's  activi- 
ties is  supposed  to  be  exterior  to  the  mind,  then  we  suppose 
two  unknown  realities — mind  which  cognizes,  and  the  unknown 
something  which  first  induces  sensations.  This  is  the  system 
of  ideal  dualism  of  Kant.  Or  we  may  suppose  the  cause  of  sen- 
sation to  be  interior — the  result  of  the  mind's  own  spontaneous 
activities.  We  then  have  the  system  of  subjective  idealism, 
that  of  Fichte.  If  we  suppose  the  cause  of  the  sensation  to  be 
the  infinite  and  absolute,  and  that  all  perception  pertains  to 
said  reality  in  its  efforts  of  self-development,  then  we  have  the 
doctrine  of  pantheism  as  developed  by  Schilling.  If,  finally,  we 
assume  that  there  is  an  absolute  identity  of  being  and  knowing, 
that  is,  assume  thought  itself  to  be  the  exclusive  object  of  pre- 
sentative knowledge,  then,  as  disciples  of  Hegel,  we  are  to  hold 
the  doctrine  of  pure  idealism. 

Now  one  or  the  other  of  the  above-named  theories  of  exist- 
ence must  be  true,  because  none  others  are  conceivable  or  pos- 
sible. In  determining  which  of  these  theories  is  true,  we  have 
but  one  standard  of  appeal,  to  wit,  what  are  we  conscious  of 
actually  perceiving  ?  If  we  are  actually  conscious  of  exercising 
the  functions  of  thought,  feeling,  and  volition,  on  the  one  hand, 
and  of  an  actual  presentative  perception  of  matter,  as  a  real  ex- 
ternal existence  having  extension  and  form,  on  the  other,  then 
we  are  to  hold  matter  and  mind  as  known  realities,  and  con- 
struct our  theory  accordingly,  that  is,  hold  the  doctrine  of 
realism.  If  we  are  conscious  of  a  similar  knowledge  of  matter 
only,  then  materialism  must  be  held  as  alone  true.  If,  finally, 
we  are  conscious  of  an  actual  synthesis  or  identity  of  being  and 
knowing,  that  is,  of  having  an  actual  presentative  knowledge  of 
subjective  states  exclusively,  then  we  are  to  hold  some  of  the 
forms  of  idealism.  These  are  the  exclusive  conditions  of  set- 
tling these  questions  on  scientific  grounds.     Philosophy  and 


384  logic. 

philosophers,  too,  must  be  brought  to  the  bar  of  facts,  real 
facts  of  consciousness,  and  held  to  the  strictest  account  there. 
Every  thing  must  be  settled  by  an  appeal  to  one  question, 
What  realities  are  actually  manifested  as  the  actual  objects  of 
conscious  presentative  knowledge  ?  When  this  is  done,  the 
idea  of  a  synthesis  or  identity  of  being  and  knowing,  together 
with  the  dogma  of  materialism,  will  be  forever  dissolved  and 
take  rank  among  the  vagaries  of  "  science  falsely  so  called  ;" 
while  realism  will  stand  before  the  world  as  affirmed  by  science 
as  well  as  by  the  intuitive  convictions  of  the  race — as  based 
upon  the  immovable  rock  of  truth.  We  shall  then  have  a  posi- 
tive philosophy  of  nature. 

9.  Let  us  now  suppose  that  nature,  the  universe  of  matter 
and  mind,  as  given  in  the  universal  intelligence,  stand  before 
us  as  scientifically  ascertained  and  known  realities,  and  that  we 
wish  to  know  whether  upon  similar  grounds  the  being  and 
perfections  of  God  are  affirmed  by  the  great  facts  of  creation 
which  he  out  before  us.  Here  two  hypotheses  present  them- 
selves as  alone  conceivably  and  possibly  true.  Either  these 
facts  are  the  exclusive  result  of  powers  and  laws  inhering  in  . 
nature,  or  of  a  power  out  of  and  above  nature.  Then  our  next 
step  is  to  determine  our  formulas,  that  is,  to  determine  what 
facts,  material  and  mental,  if  found,  would  affirm  the  truth  of 
the  theistic  hypothesis,  and  then  determine  whether  the  great 
facts  of  the  universe  do  or  do  not  rank  under  those  formulas, 
and  thus  upon  scientific  grounds  affirm  the  being  and  perfec- 
tions of  God.  If  we  find  that  they  do — and  we  shall,  if  our  in- 
vestigations are  rightly  conducted — we  then,  not  only  as  de- 
manded by  the  intuitive  convictions  of  the  race,  but  by  the  im- 
mutable principles  of  science,  erect  our  altar  to  the  '•'•Known 
God,"  and  "  knoicing  God,  we  worship  him  as  God." 

10.  The  reality  of  mind,  finite  and  infinite,  being  admitted  as  " 
a  truth  of  science,  the  question  of  the  soul's  eternity  or  of  the 
truth  of  the  doctrine  of  immortality  arises.  How  shall  this 
question  be  answered  ?  On  reflection  every  one  will  perceive 
that  science  requires  us  to  lay  down  as  the  basis  of  our  deduc- 
tions the  principle,  that  every  sentient  existence,  owing  its  be- 


APPLIED     LOGIC.  385 

ing  as  it  does  to  infinite  and  infallible  wisdom,  was  created 
for  a  certain  destiny;  that  its  powers  and  susceptibilities  are 
in  fixed  and  immutable  adaptation  to  that  destiny,  and  that, 
consequently,  the  destiny  of  each  creature  is  as  his  manifest 
powers  and  adaptations.  If  on  investigation  we  find  in  the 
human  mind  the  elements  of  endless  progression,  together 
with  the  idea  of  immortality,  and  a  nature  immutably  corre- 
lated to  it,  then  the  doctrine  of  immortality  becomes  a  truth 
of  science. 

11.  If  we  desire  to  ascertain  upon  scientific  grounds,  aside 
from  the  teachings  of  inspiration,  whether,  as  an  immortal  be- 
ing, man's  immortality  is  or  is  not  to  be  a  state  of  retribution, 
we  are  then  to  dismiss  entirely  all  assumptions  based  upon  what 
we  might  desire  to  have  true,  or  upon  what  we  might  abstract- 
ly think  it  fitting  in  the  Most  High  to  do.  "We  are,  on  the 
other  hand,  to  take  our  stand  amid  the  great  facts  of  our  moral 
nature,  and  lay  down  these  as  they  are,  as  the  exclusive  basis 
of  our  deductions.  Do  the  ideas  of  right  and  wrong,  of  obliga- 
tion, of  merit  and  demerit,  and  of  consequent  retribution,  as  a 
matter  of  fact,  exist  in  the  mind  ?  and  if  so,  what  are  their  ac- 
tual characteristics  ?  Further  :  what,  as  a  matter  of  fact,  is  the 
tendency  of  individual  progression  ?  Is  it  from  a  state  of 
changeableness  to  one  of  fixedness  in  good  or  evil  ?  If  so,  such 
is  the  state  towards  which  we  are  advancing. 

12.  Finally,  having  determined  the  objects  and  the  sphere  of 
the  thinkable,  the  great  object  of  "  the  Positive  Philosophy" 
will  then  be  to  fix  and  define  the  number,  the  sphere,  and  ob- 
jects of  the  various  sciences,  to  determine  the  nature  of  the 
great  problems  to  be  solved  by  each,  and  to  give  the  formulas 
which  lie  at  the  basis  of  their  solution.  In  what  we  have  said 
previously,  we  have  anticipated  some  subjects  which  belong  to 
the  particular  subjects  just  named. 

We  leave  these  thoughts  as  they  are,  with  the  remark,  that 
when  science  shall  proceed  exclusively  upon  such  a  basis,  its 
teachings  throughout  will  all  be  positive,  and  its  entire  deduc- 
tions will  be  the  revelations  of  immutable  truth.  A  "  Positive 
Philosophy"  is  possible,  for  the  reason  that  the  intelligence  as  a 
17 


faculty  exists  in  the  midst  of  realities  sustaining  to  it  the  rela- 
tions of  objects  of  real  knowledge. 

FALSE   METHODS   IN   PHILOSOPHY. 

"  As  is  the  method  of  a  philosopher,"  says  Cousin,  "  so  will 
be  his  system  ;  and  the  adoption  of  a  method  decides  the  des- 
tiny of  a  philosophy," — a  maxim  of  fundamental  importance. 
We  close  the  present  treatise  with  an  example  of  method  in 
this  science,  and  with  a  few  thoughts  upon  the  same.  Krug, 
the  successor  of  Kant,  and  one  of  the  great  expounders  of  the 
transcendental  philosophy,  thus  commences  his  own  treatise  on 
"  Fundamental  Philosophy :" 

"  I  put  myself,  when  I  begin  to  philosophize,  into  the  state 
of  not-knowing,  since  I  am  to  produce  in  me  for  the  first  time 
a  knowledge." — "  I  accordingly,"  he  adds,  "  regard  all  my  pre- 
vious knowledge  as  uncertain,  and  strive  after  a  higher  know- 
ledge that  shall  be  certain  or  be  made  so." 

Here,  then,  is  an  end  proposed  to  be  attained,  and  a  method 
also  of  obtaining  that  end.  The  end  proposed  is  to  ''''produce 
a  knowledge"  which  is  certain.  The  method  of  obtaining  it  is, 
to  assume  that  all  we  now  know  is  uncertain,  and  then  to  enter 
upon  the  process  of  production.  What  will  and  what  must  be 
the  result  of  such  a  procedure,  or  the  character  of  the  thing 
produced  ?  It  will  and  must,  of  course,  be  a  realization  of  the 
author's  presupposed  conceptions  of  what  that  knowledge  is, 
and  nothing  else.  To  produce,  and  to  interpret  what  is,  are 
very  different  things.  In  the  former  process  we  select  our  own 
materials,  and  impart  what  form  to  the  building  we  please.  So 
if  Mr.  Krug  previous  to  this  act  of  dementation — in  which,  with- 
out evidence,  he  arbitrarily  assumed  that  all  his  previous  know- 
ledge was  uncertain — was  a  materialist,  the  system  produced, 
as  having  appodictic  certainty,  would  be  materialism.  If  he 
was  an  idealist,  of  course  he  would  lay  at  the  basis  of  his  super- 
structure the  principle  of  "  a  synthesis,"  or  "  identity  of  being 
and  knowledge  in  the  I,"  and  thus  rear  up  some  of  the  super- 
structures of  idealism.      Nothing  in  the  world  is  so  easy  aa 


APPLIED     LOGIC.  387 

"producing  a  knowledge"  by  such  a  method.  Any  man  of 
common  ingenuity  can  produce  to  order,  in  any  form  and  to 
any  extent  required,  systems  of  this  kind.  But  what  claims 
have  such  productions  to  be  regarded  as  valid  systems  of  know- 
ledge ?  No  more  than  the  wildest  vagaries  of  the  maniac  have 
to  be  thus  regarded.  Yet  it  is  precisely  such  a  method  as  this 
that  lies  exclusively  at  the  basis  of  all  forms  of  materialism,  on 
the  one  hand,  and  of  idealism,  on  the  other.  All  these  systems 
without  exception  rest  upon  mere  arbitrary  assumptions — as- 
sumptions which  will  not  stand  a  scientific  scrutiny  for  a  single 
hour.  Idealism  especially,  in  all  its  forms,  begins  with  the  prin- 
ciple, that  to  philosophize  is  to  "produce  a  knowledge,"  and 
that  the  exclusive  method  of  production  is  to  assume  that  what 
is  now  known  is  wholly  uncertain,  and  then  to  lay  down  as- 
sumptions which  will  yield  the  deductions  which  the  subject 
desires  to  reach,  and  finally  to  construct  his  system  according- 
ly. Transcendentalists  are  great  system-makers  ;  but  not  one 
of  them  has  any  claims  whatever  to  be  regarded  as,  in  any 
proper  sense,  a  world-expounder. 


fUHIVBRSiry) 


THE    END. 


BECOMMENDATIONS  OF  DAVIES'  MATHEMATICS. 


Da  vies'  Course  of  Mathematics  are  the  prominent  Text-Books  in  mosl 
of  tlie  Colleges  of  the  Untied  States,  and  also  in  the  various  Schocls  at  i 
Academies  throughout  the  Union. 

Yokk,  Pa.,  Aug.  28,  185S. 

Dames'1  Series  of  Mathematics  I  deem  the  very  best  I  ever  saw.  From  a  number 
of  authors  I  selected  it,  after  a  careful  perusal,  as  a  course  of  study  to  be.  pursued  V>y 
the  Teachers  attending  the  sessions  of  the  York  Co.  Normal  School  -believing  it  also 
to  b*  well  adapted  to  the  wants  of  the  schools  throughout  our  country.  Already  two 
hundred  schools  are  supplied  with  Daviks'  valuable  Series  of  Arithmetic* ;  and  1 
tolly  believe,  that  in  a  very  short  time  the  Teachers  of  our  country  en  masse  will  b* 
wigaged  in  imparting  instruction  through  the  medium  of  this  new  and  easy  method 
»f  analysis  of  numbers.  A.  K.  BLAIR, 

Principal  of  York  Co.  Normal  School. 

Jackson  Union  School.  Michigan,  Sept.  25,  1S5S. 
Mkssrs.  A.  8.  Barnes  &  Co. :— I  take  pleasure  in  adding  my  testimony  in  favor  ol 
Davies'  Series  of  Mathematics,  as  published  by  you.  We  have  used  these  works  in 
this  school  for  more  than  four  years;  and  so  well  satisfied  are  we  of  their  superiority 
over  any  other  Series,  that  we  neither  contemplate  making,  nor  desire  to  make,  any 
change  in  that  direction.    Yours  truly,  E.  L.  EIPLEY. 

Nbw  Britain,  June  \2lh,  1858. 
Messrs.  A.  S.  Barnes  &  Co. :— I  have  examined  Davies'  Series  of  Arithmetics 
with  some  care.  They  appear  well  adapted  for  the  different  grades  of  schools  for 
which  they  are  designed.  The  language  is  clear  and  precise;  each  principle  is 
thoroughly  analyzed,  and  the  whole  so  arranged  as  to  facilitate  the  work  of  instruc- 
tion. Having  observed  the  satisfaction  and  success  with  which  the  different  books 
have  been  used  by  eminent  teachers,  it  gives  me  pleasure  to  commend  them  to  others. 
DAVID  N.  CAMP,  Principal  of  Conn.  State  Normal  School. 

I  have  long  regarded  Paries'  Series  of  Mathematical  Text-Books  as  far  superioi 
to  any  now  before  the  public.  We  find  them  in  every  way  adapted  to  the  wants  of 
the  Normal  School,  and  we  use  no  other.  A  unity  of  system  and  method  runs  through- 
out  the  series,  and  constitutes  one  of  its  great  excellences.  Especially  in  the  Arith- 
metics the  author  has  earnestly  endeavored  to  supply  the  wants  of  our  Common  and 
Union  Schools:  and  his  success  is  complete  and  undeniable.  I  know  of  no  Arith- 
metics which  exhibit  so  clearly  the  philosophy  of  numbers,  and  at  the  same  time  lead 
the  pupil  surely  on  to  readiness  and  practice.  A.  S.  WELCH. 

From  Phof.  G.  W.  Plympton,  late  of  the  State  Normal  School,  N.  Y. 
'  Out  of  a  great  number  of  Arithmetics  that  I  have  examined  during  the  past  year,  1 
find  none  that  will  compare  with  Davie*'  Intellectual  and  Dories'  Analytical  and 
Practical  Arithmetics,  in  clearness  of  demonstration  or  philosophical  arrangement 
I  shall  with  pleasure  recommend  the  use  of  these  two  excellent  works  to  those  who 
go  from  our  institution  to  teach. 

From  C.  May,  Jr.,  School  Commissioner,  Keene,  N.  H. 
I  have  carefully  examined  Davies'  Series  of  Arithmetics,  and  Higher  Mathe- 
nsider  them  far  superior  to  any  with  which 

sor  of  Mathematics,  Natural  Philosophy,  awl 
i  Wabash  College,  Indiana. 

Wabash  College,  June  22, 1S58. 
Mkssrs.  A.  S.  Barnes  &  Co. :— Gentlemen:  Every  text-book  on  Science  proporly 
consists  of  two  parts— the  philosophical  and  the  il/ustratire.  A  proper  combination 
of  abstract  reasoning  and  practical  illustration  is  the  chief  excellence,  in  Prof.  Davie*1 
Mathematical  Works.  I  prefer  his  Arithmetics,  Algebras.  Geometry,  and  Trigonom- 
etry, to  all  others  now  in  use.  and  cordially  recommend  them  to  all  who  desire  the 
advancement  of  sound  learning,     Yours,  very  truly,  JOHN  L.  CAMPBELL. 


"In  the  distinctness  wiih  which  the  various  definitions  are  given,  the  clear  and 
rtrictly  mathematical  demonstration  of  the  rules,  the  convenient  form  and  well-chosen 
ir.ntter  of  the  tables,  as  well  as  in  the  complete  and  much-desired  application  of  all  to 
the  business  of  the  .  juntry,  the  University  Arithmetic  of  Prof.  Davies  is  si  perior  to 
any  other  work  of  the  kind  with  which  we  are  acquainted" 


RECOMMENDATIONS 

OF 

CLARK'S  ENGLISH  GRAMMAR. 


not  better  set  forth  the  merits  of  this  work  than  by  quoting  a  part  of  a  com- 
_..   n  from  Prof.  K.  S.  .Tewkll,  of  the  New  York  State  Normal  School,  in  wbick 
school  this  Grammar  is  now  used  as  the  text  book  on  this  subject : — 

-Clark's  Systkm  op  Grammar  is  worthy  of  the  marked  attention  of  the  friends  Oi 
jducation.  Its  points  of  excellence  are  of  the  most  decided  character,  and  will  nei 
toon  be  surpassed.     Among  them  are — 

1st  "The  justness  of  Its  ground  principle  of  classification.  There  is  no  simple,  phil- 
osophical, and  practical  classification  of  the  dements  of  language,  other  than  that  buill 
i.!!  their  use  or  office.  Our  tendencies  hitherto  to  follow  the  analogies  of  the  classical 
languages,  and  classify  extensively  according  to  forms,  have  been  mischievous  and  ab- 
surd. It  lutlnie  we  corroded  them. 
'•  Its  thorough  and  yet 

d  power  of  the  language  can  be  attained. 

absence  of  this  analysis  has  hitherto  precipitated  the  study  of  Grammar  upon  a  surface 
of  dry  details  and  bare  authorities,  and  useless  technicalities. 

3d."  "Its  happy  method  otillustrating  the  relations  of  elements  by  diagrams.  These, 
however  uncouth  they  may  appear  to  the  novice,  are  really  simple  and  philosophical. 
Of  their  utility  there  can  he  no  question.  It  is  supported  by  the  usage  of  other  sci- 
ences and  has  been  demonstrated  by  experience  in  this. 

4th.  "The  tendency  of  the  system,  when  rightly  taught  and  faithfully  carried  out, 
to  cultivate  habits  of  nice  discrimination  and  close  reasoning,  together  with  skill  in 
Illustrating  truth.  In  this  it  b  not  excelled  by  any,  unless  it  tie  the  mathematical  sci- 
ences, and  even  there  it  has  this  advantage,  that  it  deals  with  elements  more  within 
t  grasp  of  the  intellect.  On  this  point  I  speak  advisedly, 
'he  system  is  thoroughly  progressive  and  practical,  and  as  such.  American  in 
;er.  It  does  not  adhere  to  old  usages,  merely  because  tbey  are  venerat.y 
musty;  and  yet  it  does  not  discard  things  merely  because  they  are  old,  or  are  in  un- 
important mi'nutiai  not  prudishly  perfect.  It  does  not  overlook  details  and  technicali- 
ties, nor  does  it  allow  them  to  interfere  with  plain  philosophy  or  practical  utility. 

"Let  any  ciear-headed.  independent- minded  teacher  master  the  system,  and  then 
give  it  a  fa'ir  trial,  and  there  will  be.  no  doubt  as  to  his  testimony." 

A   Testimonial  from  the  Principals  of  the  Public  Schools  of  Rochester,  N.  Y. 

We  regard  Clark's  Grammar  as  the  clearest  in  its  analysis,  the  most  natural  and 

logical  in  its  arrangement,  the  most  concise  and  accurate  in  its  definitions,  the  most 

systematic  in  design,  and  the  best  adapted  to  the  use  of  schools  of  any  Grammar  with 

which  we  are  acquainted. 

C  C.  MKSERVE,  WM.  C.  FEGLES. 

M   IX  ROWLEY,  OIIN  ATWATKR. 

C.  R.  BIT; HICK.  EDWARD  WEBSTER, 

J.  R.  VOSBURG,  S.  W.  STARKWEATHER, 

&  R.  ARMSTRONG  PHILIP  CURTISS. 

Lawrence  Institute.  Brooklyn.  .Jan.  15,  1859. 
Messrs.  A.  S.  Barnf6  &  Co:— Having  used  Clark's  \ew  Grammar  since  its  publica- 
tion, I  do  most  unhesitatingly  recommend  It  as  a  work  of  superior  merit.     By  the  use 
of  no  other  work,  and  I  have  used  several,  have  I  been  enabled  to  advance  my  pupilt 
so  rapidly  and  thoroughly. 

The  author  has,  by  "an  "Etymological  Chart  and  a  system  of  Diagrams,  made  Gram 
mar  the  study  that  it  ought  to  be,  interesting  as  well  as  useful. 

MARGARET  S.  LAWRENCE,  Prinoipai. 


ir 


WELCH'S  ENGLISH  SENTENCE. 

From  Prop.  J.  R.  Boisrc,  A.  M.,  Professor  of  the  Latin  and  Greek  Language*  and 
Literature  in  the  University  of  Michigan. 
This  work  belongs  to  a  new  era  in  the  grammatical  study  of  our  own  language.  "We 
hazard  nothing,  in  expressing  the  opinion,  that  for  severe,  searching,  and  exhaustive 
analysis,  the  work  of  Professor  Welch  is  second  to  none.  His  book  is  not  intended  fot 
beginners,  but  only  for  advanced  students,  and  by  such  only  it  will  be  understood  and 
»pproeiat*d. 


RECOMMENDATIONS 

or 

PARKER  &  WATSON'S  READERS 


From  Prop.  Frederick  S.  Jewell,  of  the  New  York  State  Normal  School 
It  gives  me  pleasure  to  find  in  the  National  Series  of  School  Readers  ample  i^^» 
fcr  commendation.     From  a  brief  examination  of  them,  I  am  led  to  believe  tilt'  «r» 
have  none  equal  to  them.    I  hope  they  will  prove  as  popular  as  tboy  are  excellent 

From  Hon.  Theodore  Frelinghuyskn,  President  of  Rutgers"  College,  N  J. 
A  cursory  examination  leads  me  to  the  conclusion  that  the  syetem  contained  ta 
these  volumes  deserves  the  patronage  t>f  our  schools,  and  I  have  no  doubt  that  it  will 
become  extensively  used  iu  the  education  of  children  and  youth. 

From  N.  A.  Hamilton,  President  of  Teachers"  Union,  Whitewater,  Wis. 

The  National  Readers  and  Speller  I  have  examined,  and  carefully  compared  with 

others,  and  must  pronounce  them  decidedly  superior,  in  respect  to  literary  merit, 

»tyle,  and  price.    The  gradation  is  more  complete,  and  the  series  much  more  desirable 

for  use  in  eur  schools  than  Sanders'  or  McGuffey's. 

From  Prof.  T.  F.  Thickstun,  Principal  of  Academy  and  Normal  School, 
Meadville,  Pa. 
1  am  much  pleased  with  the  National  Series  of  Readers  after  having  canvassed 
their  merits  pretty  thoroughly.  The  first  of  the  series  especially  pleases  me,  because 
It  affords  the  means  of  teaching  the  " word -method"  in  an  appropriate  and  natural 
manner.  They  all  are  progressive,  the  rules  of  elocution  are  stated  with  clearness, 
and  the  selection  of  pieces  is  such  as  to  please  at  the  same  time  that  they  instruct 

From  J.  W.  Schermerhorn,  A.  B.,  Principal  Coll.  Institute,  Middletown,  N.  J. 
I  consider  them  emphatically  the  Readers  of  the  present  day,  and  I  believe  thtt 
their  intrinsic  merits  will  insure  for  them  a  full  measure  of  popularity. 

From  Peter  Rouget,  Principal  Public  School  No.  10,  Brooklyn. 
It  gives  me  great  pleasure  to  be  able  to  bear  my  unqualified  testimony  to  the  excel 
lence  of  the  National  Series  of  Readers,  by  Pakkrr  and  Watson.  The  gradation  of 
the  books  of  the  series  is  very  fine ;  we  have  reading  in  its  elements  and  in  its  highest 
atyle.  The  fine  taste  displayed  in  the  selections  and  in  the  collooation  of  the  piecet 
ieserves  much  praise.  A  distinguishing  feature  of  the  series  is  the  variety  of  the 
•ubject-matter  and  of  the  style.  The  practical  teacher  knows  the  value  of  this  charac- 
teristic for  the  development  of  the  voice.  The  authors  seem  to  have  kept  constantly 
In  view  the  fact  that  a  reading-book  is  designed  for  children,  and  therefore  they  havo 
•ucceeded  in  forming  a  very  interesting  and  improving  collection  of  reading-matter, 
highly  adapted  to  the  wants  and  purposes  of  the  school-room.  In  short,  I  look  upon 
the  National  Series  of  Readers  as  a  great  success. 

From  A.  P.  Harrington,  Principal  of  Union  School,  Marathon,  N.  Y. 

These  Readers,  in  my  opinion,  are  the  best  I  have  ever  examined.  The  rhetorical 
oxercises,  in  particular,  are  superior  to  any  thing  of  the  kind  I  have  ever  seen.  I  havo 
had  better  success  with  my  reading  classes  since  I  commenced  training  them  on  these 
than  I  ever  met  with  before.  The  marked  vowels  in  the  reading  exercises  convey  to 
the  reader's  mind  at  once  the  astonishing  fact  that  he  has  been  accustomed  to  mispro- 
nonnce  more  than  one-third  of  the  words  of  the  English  language. 

From  Charles  S.  Halsey,  Principal  Collegiate  Institute,  Newton,  N.  J. 

In  the  simplicity  and  clearness  with  which  the  principles  are  stated,  in  the  appro 
priatenees  of  the  selections  for  reading,  and  in  the  happy  adaptation  of  the  ditfeient 
parts  of  the  series  to  each  other,  these  works  are  superior  to  any  other  text-books  on 
oii»  aubject  which  I  have  examined. 

From  "William  Tratib,  Principal  of  Union  School,  Flint,  Mich. 
I  hive  examined  the  National  Series  of  Readers,  and  am  delighted  to  find  it  so  far 
ta  advance  of  most  other  series  now  in  use,  and  so  well  adapted  to  the  wants  of  the 
f  dbii*  Schools.     It  is  unequaled  in  the  skillful  arrangement  of  the  material  used, 
beautiful  typography,  and  tl 
souks.     I  predict  for  it  a  core 
most  enterprising  toichers. 


IIIONTEITH  AND  McNALLTTS  GEOGRAPHIES: 

THE  MOST  SUCCESSFUL  SERIES  EVER  ISSUER 


RECOMMENDATIONS. 

A.  B.  Clark,  Principal  of  one  of  the  largest  Public  Schools  in  Brooklyn,  s*ys:— 
"I  have  used  over  a  thousand  copies  of  Monteith's  Manual  of  Geography  since  tti 
adoption  by  the  Board  of  Education,  and  am  prepared  to  say  it  is  the  best  work  tot 
Junior  and  intermediate  classes  in  our  schools  I  have  ever  seen." 


The  Series,  in  whole  or  in  part,  has  been  adopted  in  the 


New  York  State  Normal  School. 
New  York  City  Normal  School. 
New  Jersey  State  Normal  SchoeL 
Kentucky  State  Normal  School. 
Indiana  State  Normal  School. 
Ohio  State  Normal  School. 
Michigan  State  Normal  School. 
York  County  (Pa.)  Normal  BchooL 
Brooklyn  Polytechnic  Institute. 
Cleveland  Female  Seminary. 
Public  Schools  of  Milwstikio. 
Public  Schools  of  Pittsburgh. 
Public  Schools  of  Lancaster,  Pa. 
Public  Schools  of  New  Orleans. 


Public  Schools  of  New  York. 
Public  Schools  of  Brooklyn,  L.  L 
Public  Schools  of  New  Haven. 
Public  Schools  of  Toledo,  Ohio. 
Public  Schools  of  Norwaik,  Conn. 
Public  Schools  of  Richmond.  Va. 
Public  Schools  of  Madison,  Wis. 
Public  Schools  of  Indianapolis. 
Public  Schools  of  Springfield,  Mass. 
Public  Schools  of  Columbus.  Ohio. 
Public  Schools  of  Hartford.  Conn. 
Public  Schools  of  Cleveland,  Ohio. 

And  other  places  too  numerous  to 
mention. 


They  have  also  been  recommended  by  the  State  Superintendents  of  Illinoib, 
Indiana,  Wisconsin,  Missouri,  Noutii  Carolina,  Alabama,  and  by  numerous 
Teachers'  Associations  and  Institutes  throughout  the  country,  and  are  in  successful 
use  in  a  multitude  of  Public  and  Private  Schools  throughout  the  United  States. 


From  Prof.  Wm.  F.  Phelps,  A.  M„  Principal  of  the  New  Jersey  State 
Normal  Softool. 

Trentok,  June  17, 1868. 
Messrs.  A.  S.  Barnes  &  Co. :— Gentlemen  :  It  gives  me  much  pleasure  to  state 
that  McNally's  Geography  has  been  used  in  this  Institution  from  its  organization  In 
1855,  with  great  acceptance.  The  author  of  this  work  has  avoided  on  one  hand  the 
extreme  of  being  too  meager,  and  on  the  other  of  going  too  much  into  detail,  while 
he  has  presented,  in  a  clear  and  concise  manner,  all  those  leading  fucts  of  Descriptive 
Geography  which  it  is  important  for  the  young  to  know.  The  maps  are  accurate  and 
welf executed,  the  type  clear,  and  indeed  the  entire  work  is  a  decided  success.  I  most 
cheerfully  commend  it  to  the  profession  throughout  the  country. 

Very  'July  yours,  WM.  F.  PHELPS. 

From  W.  V.  Davis,  Principal  of  High  School,  Lancaster,  Pa. 

Lancaster,  Pa.,  June  26,  1858. 

Dear  Sirs  : — I  have  examined  your  National  Geographical  Series  with  much 
care,  and  find  them  most  excellent  works  of  their  kind.  Tliey  have  been  used  in  the 
various  Public  Schools  of  this  city,  ever  since  their  publication,  with  great  success  and 
satisfaction  to  both  pupil  and  teacher.  All  the  Geographies  embraced  in  your  series 
are  well  adapted  to  school  purposes,  and  admirably  calculated  to  impart  to  the  pupil, 
in  a  very  attractive  manner,  a  complete  knowledge  of  a  science,  annually  becoming 
more  useful  and  important.  Their  maps,  illustrations,  and  typography,  are  unsur- 
passed. One  peculiar  feature  of  McNally's  Geography — and  which  will  recommend 
it  at  once  to  every  practical  teacher— is  the  arrangement  of  its  maps  and  lessons ; 
each  map  fronts  the  particular  lesson  which  it  is  designed  to  illustrate— thus  enabling 
the  scholar  to  prepare  his  task  without  that  constant  turning  over  of  leaves,  or  refer- 
ence to  a  separate  book,  as  is  necessary  with  most  other  Geographies.    Yours.  &c. 

Messrs.  A.  S.  Barnes  &  Co.,  New  York.  V.  W.  DAVI8. 

From  Charles  Barnes,  late  President  State  Teachers'  Association,  and  Superin- 
tendent of  the  Public  Schools  at  New  Albany,  Indiana. 
Messrs.  A.  S.  Barnes  &  Co. :— Dear  Sirs  :  I  have  examined  with  considerable 
eare  the  Series  of  Geographies  published  by  you,  and  have  no  hesitation  in  saying 
that  it  is  altogether  the  best  with  which  I  am  acquainted.  A  trial  of  more  than  a 
year  in  the  Public  Schools  of  this  eity  has  demonstrated  that  Cornell  is  utterlv  unfit 
for  the  school-room.    Yours,  &c  a  BARNES. 


RECOMMENDATIONS 
FEOK'S      GANOT. 


From  the  New  Fnalander. 

As  an  elementary  work,  it  is  concise  in  style,  yet  remarkably  clear  in  definitions 
and  explanations,  h.gical  in  arrangement,  and  beautifully  illustrated  with  numerous 
engravings.  These  engravings  are  so  complete  and  accurate  that  they  are  not  only 
well  calculated  to  convey  to  the  mind  of  the  pupil  a  clear  conception  of  the  prin- 
ciples unfolded,  but  exhibit  so  full  the  structure  of  apparatus  and  methods  of  exper- 
imenting, as  to  render  the  apparatus  Itself  in  many  eases  unnecessary.  Prof.  Peck 
lias  done  a  good  thing  for  American  education  in  producing  so  attractive  and  excel- 
lent a  book. 

From  the  New  York  Teacher. 

We  were  particularly  pleased  witli  the  beauty  of  the  engravings.  They  are,  by 
tar,  the  most  satisfactory  of  any  that  have  appeared  in  works  of  this  elass'and  many 
of  them  are  gems  of  art.  The'book  itself  redeems  all  the  promises  thai  were  made 
for  it,  prior  to  its  appearance.  It  is  clear  and  concise  in  definitions,  logical  in 
arrangement,  and  full  and  exhaustive  in  descriptions.  The  illustrations  of  prin- 
ciples and  detail  of  philosophical  experiments  leave  little  to  be  desired  except  what 
the  reader  himselt  will  be  impelled  to  discover.  The  science  is  made  attractive,  and 
the  clearness  of  statement  where  a  principle  or  law  is  enunciated  will  be  appreci- 
ated by  both  teacher  and  pupil.  The  practical  Illustrations  in  the  work  will  com- 
mend it  to  all  who  look  for  tangible  results.  A  too  common  'ault  in  our  school 
philosophies  is  their  abstract  character.  Mr.  Peck  has  added  to  the  other  excel- 
lences it  possesses  a  felicity  of  language  which  will  attract  the  scholar  and  the  tyro 
alike.     We  think  it  will  be  found  a  \  alualile  contribution  to  this  branch  of  science. 


PORTER'S    CHEMISTRY. 

By  Professor  Porter,  of  Yale  College:  the  most  Practical  and  Popular  Scientific 
Work  ever  published. 
From  the  Amer.  Journal  of  Education,  Hartford. 
We  have  examined  it  with  reference  to  its  qualities  as  a  school-book,  its  adaptation 
to  the  wants  of  beginners  in  the  study  of  a  science  which  to  many,  even  of  College 
students,  is  as  obscure  in  nomenclature  and  symbols  as  it  is  brilliant  in  demonstra- 
tions.    As  a  text-book  for  the  higher  classes  in  schools  and  academies,  we  regard  the 
work  as  deserving  of  high  praise.     The  language  is  clear  and  concise,  the  illustrations 
are  well  chosen,  and  the  arrangement  of  topics  is  natural  and  methodic.    While  the 
technical  terms  of  chemistry  are  explained  sufficiently  to  introduce  the  student  to 
more  extended  treatises  in  the  science,  they  are  not  employed  so  much  as  to  impede 
his  progress  at  the  outset  of  his  course. 


FIRST   BOOK   OF  SCIENCE. 

By  Professors  Norton  and  Porter,  of  Yale  College. 

Office  of  Superintendent  of  Schools,  Buffalo,  Feb.  27, 1559. 
Messrs.  A.  8.  Barnes  &  Co. :— Gkntt.emen  :  I  have  examined  with  much  interest 
the  "First  Book  of  Science,"  by  Professors  Porter  and  Norton,  and  I  am  free  to  say 
that  it  is  admirably  designed  to  meet,  a  want  in  the  Public  Schools.  Comparatively 
few  of  those  who  attend  "our  Common  Schools  remain  long  enough  to  gain  any  valu- 
able knowledge  of  Philosophy.  Chemistry,  and  the  Allied  Sciences;  and  the  text- 
books on  these  subjects  which  hive  been  in  use  hitherto  are  too  abstruse  and  cumber- 
some for  the  young  scholar.  I  should  regard  the  introduction  of  this  book  f.s  the  best 
means  of  exciting  popular  interest  in  the  Natural  Sciences,  and  of  trivial:  pupils  who 
cannot  pursue  a  "course  of  study  much  desirable  and  practical  information  upon  the 
subjects  treated.  I  am  confident  it  will  commend  itself  to  the  attention  of  the  friend* 
of  education  throughout  the  country.    Respectfullv  vonrs. 

JOSEPH  WARREN    Sup't  of  Schoolt 


LOAN  DEPT. 

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